OPINION
Michael Massengale, JusticeAppellants Richard and Connie Rogge sued the City of Richmond after their son committed suicide in a jail cell. The City filed a plea to the jurisdiction and a motion for summary judgment asserting governmental immunity. In response, the Rogges argued that immunity had been waived under the Texas Tort Claims Act. See Tex. Civ. PRAC. & Rem. Code §§ 101.001-.109. The trial court granted the City’s motion.
The Rogges’ suit is classified as a premises-liability claim based on allegations that their son’s death was caused by a defective metal grate covering an air vent on the ceiling of the jail cell. But no evidence suggests that the metal grating was inherently dangerous or hazardous in its intended use as a cover for the air vent. Moreover, no evidence suggests that the condition of the grate actually caused the Rogges’ son to commit suicide. We conclude that statutory waiver of governmental immunity for death caused by a condition of real property did not apply to this case, and the court lacked subject-matter jurisdiction over the Rogges’ claims. Accordingly, we affirm.
Background
Richard Hollas Rogge was arrested for driving while intoxicated. He was taken to the City of Richmond police station, where he was placed in a holding cell while the *573arresting officer completed the paperwork required to transfer him to the Fort Bend County jail. Video recordings from inside the holding cell showed Rogge lying on a bench, apparently napping for the majority of the time he spent there. It is undisputed that Rogge was left alone in the cell for approximately three hours while no officer physically checked on him. During that time, Rogge committed suicide by using his shirt to hang himself from a metal grate covering an air vent.
Rogge’s parents (hereinafter, the Rogg-es) sued the City of Richmond and two of its police officers alleging civil rights violations under federal law arid causes of action under the Texas Tort Claims Act. The defendants removed the case to federal court for prosecution of the civil rights claims. The federal district court entered a take-nothing judgment on those causes of action and remanded the remaining state-law claims to the district court of Fort Bend County,
In state court, the Rogges alleged negligence, wrongful-death, and survival claims. They contended that their son’s death was caused by the use or condition of property—the metal grate—-which was “affixed into the ceiling and positioned] directly above a toilet located in the holding cell.” They alleged that the metal grate presented an unreasonable risk of harm because it was easily accessible to a person who wanted to harm himself. In the alternative, they pleaded that the positioning of the vent above the toilet was a premises defect.
The City filed a plea to the jurisdiction and motion for summary judgment, asserting that all of the Rogges’ claims were barred by governmental immunity. The City argued that the suicide was not caused by a condition or use of tangible property, see Tex. Civ. Pbac. & Rem. Code § 101.021(2), and that the claims were barred by the discretionary-function exception to the limited waiver of immunity found in the Tort Claims Act, see id. § 101.056.
The Rogges amended their petition, and they responded to the jurisdictional challenge with evidence, including a preliminary report and deposition excerpts from an architect with expertise in the design and construction of jails and holding cells. In addition, the Rogges argued that the discretionary-function exception to the Tort Claims Act’s limited waiver of immunity was irrelevant because they alleged a premises defect based on the size of the holes in the metal grate and its lack of mesh backing, as opposed to a claimed defect in the design of the holding cell itself.
The trial court granted summary judgment in favor of the City, and the Rogges appealed.
Analysis
The Rogges challenge the dismissal of their lawsuit in four issues, arguing that (1) their son’s death was caused by the City’s usé of tangible personal property, (2) his death was caused by a condition of tangible personal property, (3) the discretionary-function exception to the waiver of immunity did not apply, and (4) their cause of action for a premises defect was not addressed. by the motion for summary judgment.
Governmental immunity from suit defeats a trial court’s subject-matter jurisdiction, and it may be asserted in a plea to the jurisdiction or a motion for summary judgment. See Tex. Dep’t of Parks & Wildlife v. Miranda, 133 S.W.3d 217, 225-26 (Tex.2004); Bland Indep. Sch. Dist. v. Blue, 34 S.W.3d 547, 554 (Tex.2000). Whether a trial court has subject-matter jurisdiction is a question of law, *574which we review de novo. See Miranda, 133 S.W.3d at 226.
A plaintiff must allege facts that affirmatively establish the trial court’s subject-matter jurisdiction. State v. Holland, 221 S.W.3d 639, 642 (Tex.2007). In determining whether the plaintiff has satisfied this burden, we construe the pleadings liberally in the plaintiffs favor and deny the plea if facts affirmatively demonstrating jurisdiction have been alleged. Id. at 643; Miranda, 133 S.W.3d at 227.
When a defendant challenges the sufficiency of jurisdictional facts, the trial court must consider relevant evidence submitted by the parties. City of Waco v. Kirwan, 298 S.W.3d 618, 622 (Tex.2009); Miranda, 133 S.W.3d at 227. In doing so, the court will “take as true all evidence favorable to the nonmovant” and “indulge reasonable inferences and resolve doubts in her favor.” Miranda, 133 S.W.3d at 228. When the relevant evidence is undisputed or fails to raise a fact question on the jurisdictional issue, the trial court rules on the plea to the jurisdiction as a matter of law. Id. at 228. If, however, the evidence creates a fact question regarding jurisdiction, then the trial court must deny the plea, and the fact issue will be resolved by the factfinder. Id. at 227-28.
The doctrine of governmental immunity, like sovereign immunity from which it is derived, protects political subdivisions of the State from lawsuits unless the Legislature specifically has waived its immunity to suit. See City of Houston v. Williams, 353 S.W.3d 128, 134 (Tex.2011). The Tort Claims Act, which provides a limited waiver of immunity, applies equally to the State and its political subdivisions, including cities. Mission Consol. Indep. Sch. Dist. v. Garcia, 253 S.W.3d 653, 655 (Tex.2008); see Tex. Civ. PRAC. & Rem. Code § 101.001(3). Among other categories of permitted, claims, section 101.021 waives sovereign immunity in premises-defect cases, which represent a specific type of case arising from a condition of real property. See, e.g., Cty. of Cameron v. Brown, 80 S.W.3d 549, 554 (Tex.2002); see also Tex. Civ. Prao. & Rem. Code §§ 101.021(2), 101.022(a). Immunity is waived for “personal injury and death” proximately caused “by a condition or use of tangible personal or real property if the governmental unit would, were it a private person, be liable to the claimant according to Texas law.” Tex. Civ. Prao. & Rem. Code § 101.021(2).
In the trial court; the Rogges pleaded alternative causes of action. First, they alleged that “a metal grate affixed into the ceiling” and positioned “directly above a toilet located in the holding cell” was a “condition of the premises” constituting a premises defect that “placed an unreasonable risk of harm ... as the grate was easily accessible by a person to cause or inflict harm to himself.” They further alleged that the City had “actual knowledge of the premises defect,” that it was “aware that such defect was a dangerous condition,” and that the dangerous condition was created by the City “through the design and use of the premises.” The Rogges contended that the City .breached its duty to their son by creating “the dangerous condition,” failing to warn about the condition, and failing to make it reasonably safe, proximately resulting in the suicide. The Rogges also alleged negligence “in supplying” tangible personal property, identified in the trial court and on appeal as the metal grate on the ceiling.1 The grate was *575alleged to be “inadequate,” “defective,” and missing “necessary and integral” safety components.
The Rogges relied upon both the premises-liability and’ negligence theories of liability to support wrongful death and survival claims. On appeal, the Rogges base each of these claims on the “use” and “condition” of the metal grate, which they alleged was the cause of their son’s suicide.
I. Classification of cause of action
To decide the jurisdictional issue presented by this appeal, we first must evaluate how to characterize the Rogges’ cause of action. The Tort Claims Act imposes different standards of care upon a governmental unit for negligence claims based on “a condition or use of tangible personal property” and claims based on a “premises defect” relating to the condition or use of real property. See Sampson v. Univ. of Tex. at Austin, No. 14-0745, 500 S.W.3d 380, 384-85, 2016 WL 3212996, at *2 (Tex. June 10, 2016) (citing Tex. Civ. PkaC. & Rem. Code §§ 101.021(2), 101.022(a)). A claim cannot be both a premises-defect claim and also a claim relating to a condition or use of tangible property. See id. at 385-86, 2016 WL 3212996, at *3 (citing Miranda, 133 S.W.3d at 233). ‘Whether a claim is based on a premises defect is a legal question.” Id. 384-85, 2016 WL 3212996, at *2. A claim based on a condition or use of real property is a premises-defect claim under the Tort Claims Act. Id. at 385-86, 2016 WL 3212996, at *3 (citing Miranda, 133 S.W.3d at 230, and Tex. Civ. Prac. & Rem. Code §§ 101.021(2), 101.022).
When “liability is predicated not upon the actions of the governmental unit’s employees but by reference to the duty of care owed by the governmental unit to the claimant for premise and special defects as specified in section 101.022 of the ... Tort Claims Act,” the claim is based on an allegation of premises defects. DeWitt v. Harris Cty., 904 S.W.2d 650, 653 (Tex.1995); see also Sampson, 500 S.W.3d at 388, 2016 WL 3212996, at *4. “[N]egli-gent activity encompasses a malfeasance theory based on affirmative, contemporaneous conduct by the owner that caused the injuiy, while premises liability encompasses a nonfeasance theory based on the owner’s failure to take measures to make the property safe.” Del Lago Partners, Inc. v. Smith, 307 S.W.3d 762, 776 (Tex.2010). Thus, when distinguishing between a negligent activity and a premises defect, we must focus on “whether the injury occurred by or as a contemporaneous result of the activity itself—a negligent activity— or rather by a condition created by the activity—a premises defect.” Sampson, 500 S.W.3d at 388, 2016 WL 3212996, at *4 (citing Keetch v. Kroger Co., 845 S.W.2d 262, 264 (Tex.1992)). “The distinction lies in whether it is the actual use or condition of the tangible .personal property itself that allegedly caused the injury, or whether it is a condition, of real property— created by an item of tangible personal property—that allegedly caused the injury.” Id.
Within the Tort Claims Act’s context, “condition” has been defined as “either an intentional or an inadvertent state of being.” Id. (quoting Abutahoun v. Dow Chem. Co., 463 S.W.3d 42, 49 (Tex.2015)). To state a “condition” claim under the Tort Claims Act, there must be an allegation of *576“defective or inadequate property.” Id. Furthermore, “use” has been defined to mean “to put or bring into action or service; to employ for or apply to a given purpose.” Id. (quoting Tex. Dept. of Criminal Justice v. Miller, 51 S.W.3d 583, 588 (Tex.2001)). “As with negligent activity claims under common law, to state a ‘use’ of tangible personal property claim under the Tort Claims Act, the injury must be contemporaneous with the use of the tangible personal property—‘[ujsing that property must have actually caused the injury,”’ Id. (quoting Miller, 51 S.W.3d at 588).
A governmental unit “does not ‘use’ tangible personal property ... within the meaning of section 101.021(2) by merely providing, furnishing, or allowing ... access to it.” Id. (quoting Rusk State Hosp. v. Black, 392 S.W.3d 88, 98 (Tex.2012)). “However, non-use and furnishing access are distinguishable from situations in which a governmental unit ‘provided equipment that lacked an integral safety component.’ ” Id. (citing Tex. A&M Univ. v. Bishop, 156 S.W.3d 580, 584 (Tex.2005)).
Our determination turns on whether the contemporaneous “action or service” (use) or “state of being” (condition) of the tangible personal property itself caused- the injury, or whether the tangible personal property created a dangerous real-property condition, making it a premises defect. See id. “Just as at common law, where an activity may create a condition of the premises, under the Tort Claims Act an item of tangible personal property may create a condition of the premises, resulting in a premises defect claim.” Id. (citing Keetch, 845 S.W.2d at 264).
The Rogges rely on Retzlaff v. Texas Department of Criminal Justice, 135 S.W.3d 731 (Tex.App.-Houston [1st Dist.] 2003, no pet.), a case in which a prisoner fell into a razor-wire fence constructed on the perimeter of a prison recreation yard. This court held that the prison’s placement of the razor wire was a use of tangible personal property, and immunity had been waived by. the Tort Claims Act as to a negligence claim. Retzlaff, 135 S.W.3d at 741. The Rogges argue that the City in this case similarly “used” the grate by installing it in the holding cell for the purpose of preventing “a prisoner’s escape through the ventilation.” We find no factual support for this argument. The testimony in the appellate record addressed the need for suitably-sized holes to permit the passage of air, industry recommendations regarding identification of individuals at-risk for suicide, and methods for continuous observation of at-risk people. But the deposition excerpts relied upon by the Rogges do not include testimony that the purpose of the metal grate was to prevent a prisoner’s escape. Thus, the jurisdictional evidence does not support the comparison to Retzlaff and the suggestion that the suicide resulted from the use of the grate to prevent escape.
The Rogges also urge us to follow a precedent of the Corpus Christi Court of Appeals in Martinez v. City of Brownsville, No. 13-00-425-CV, 2001 WL 1002399 (Tex.App.-Corpus Christi Aug. 31, 2001, pet. denied) (mem. op.; not designated for publication). In Martinez, an inmate committed suicide by hanging himself with a shirt tied to the bars on his prison cell door. Martinez, 2001 WL 1002399, at *2. The court of appeals rejected the argument that the decedent’s use of tangible personal property was insufficient to satisfy the statute because the governmental entity had to use the property to waive immunity. Id. at *6-7. The court held that the City used the cell improperly by failing to provide the decedent with garments that could not have been used to commit *577suicide. Id. at *7. We acknowledge the factual similarity between Martinez and this case. In both cases, the inmates used clothing and city-owned property to commit suicide. However, we decline to follow Martinez, which is inconsistent with subsequently decided Supreme Court authority that clarified that a governmental unit does not use “property merely by allowing someone else to use it and nothing more.” San Antonio State Hosp. v. Cowan, 128 S.W.3d 244, 246 (Tex.2004) (no waiver of immunity when suicidal hospital patient committed suicide with suspenders and walker); see also Dallas Cty. v. Posey, 290 S.W.3d 869, 871-72 (Tex.2009) (per curiam) (no waiver of immunity when inmate committed suicide with a telephone cord).
We conclude that the Rogges’ claim is properly classified as a premises-defect claim, and not one based on the use of tangible personal property. This is not a case in which liability is predicated upon any “affirmative, contemporaneous conduct” by the City’s employees, Del Lago Partners, 307 S.W.3d at 776, but instead depends upon the duty of care owed by the City to people held in the police station’s holding cell. See DeWitt, 904 S.W.2d at 653; Sampson, 500 S.W.3d at 385-86, 2016 WL 3212996, at *4. Accordingly, we overrule the Rogges’ first issue, which is based on the specific theory that “the death of Richard Hollis Rogge was caused by the City’s use of tangible personal property.”
We also overrule their fourth issue, which is similarly premised on the incorrect assumption that the petition embodied distinct claims based on the City’s alleged use of tangible personal property and also based on an alleged premises defect. The claim was based on an alleged premises defect, not use of tangible personal property, see Sampson, 500 S.W.3d at 386-89, 2016 WL 3212996, at *3, and the City’s motion for summary judgment and plea to the jurisdiction properly presented the immunity defense that Rogge’s death was not caused by a defective condition of tangible property.
II. Premises-Iiability claim based on condition of tangible personal property
In their second issue, the Rogges argue that the trial court erred by dismissing their case because immunity was waived due to the condition of the metal grate, which they contend caused their son’s death.
A condition of property may be a basis for waiver of governmental immunity when it makes the property inherently dangerous and “poses a hazard when the property is put to its intended and ordinary use.” Rusk State Hosp., 392 S.W.3d at 99. When waiver of immunity is premised on a condition of property, “there must be a nexus between the condition of the property and the injury.” Posey, 290 S.W.3d at 872. “This nexus requires more than mere involvement of property; rather, the condition must actually have caused the injury.” Id. (citing Dallas Cty. Mental Health & Mental Retardation v. Bossley, 968 S.W.2d 339, 342-43 (Tex.1998)). Thus immunity may be waived when a plaintiff alleges that tbe governmental entity has provided him with property lacking an integral safety component and that the lack of such safety component caused his injuries. Rusk State Hosp., 392 S.W.3d at 99; Cowan, 128 S.W.3d at 247.
On. appeal, the Rogges contend that the metal grate’s ventilation holes were “too large” and that an “integral safety component” was lacking.2 They rely, on excerpts *578from the architect’s deposition and his report to support their claim that the ventilation holes in the metal grate were too large for use in a holding cell and that a mesh backing was required. They argue that the mesh backing was an integral safety component that the metal grate lacked.
The architect testified that contemporaneous industry recommendations promoted the use of smaller ventilation holes as an additional means to prevent suicide, along with the preferred methods of identifying at-risk individuals and closely monitoring them. He did not testify that the metal grate lacked an integral safety component. Contrary to the description in the Rogges’ brief, the deposition excerpts in the appellate record also do not show the expert testifying “that tear away clothing and/or the lack of clothing-should have-been provided to Rogge as he was intoxicated, under the influence of antidepressants and a suicide risk.” To the contrary, when asked if he would have “believed it appropriate for Mr. Rogge to have been detained in this cell with no clothes on,” the architect declined to answer, saying he lacked sufficient information and explaining other measures law enforcement officers can use to prevent inmate suicide—such as identification and monitoring of at-risk individuals.
There is no evidence in thé appellate record that the metal grating was inherently dangerous or hazardous in its intended use as a cover for the air vent. None of the jurisdictional facts show that the condition of the grate actually caused the injury. See Rusk State Hosp., 392 S.W.3d at 99; Posey, 290 S.W.3d at 872.
Our dissenting colleague suggests that the Rogges should be permitted an opportunity to replead and cure the jurisdictional defect. The pleadings already were amended in response to. the jurisdictional challenge, and the Rogges have not suggested how they would amend them pleadings. if given a second opportunity to do so. “For a defective condition to be the basis for complaint, the defect must pose a hazard in the intended and ordinary use of the property.” Posey, 290 S.W.3d at 872. Even if the pleadings were amended to allege that the intended and ordinary use of the metal grate was to preyent an inmate from escaping through the air vent, the alleged*579ly defective combination of the large holes and the lack of mesh backing would not have actually caused this injury. See id. Likewise, even if the Rogges challenged the placement of the toilet as a defective condition of real property, that would not establish that the toilet posed a hazard when put to its intended and ordinary use. See-id. Even an allegation that the metal grate, the relative placement of the toilet, and the failure to provide tear-away clothing combined to create a premises defect would not adequately allege a nexus between a dangerous condition of real property and the cause for the tragic suicide that occurred in the jail cell. See id. In the absence of an argument suggesting how the pleadings might be cured, a remand would serve no purpose. See Texas A & M Univ. Sys. v. Koseoglu, 2133 S.W.3d 835, 840 (Tex.2007).
We therefore hold that the City’s immunity was not waived' by a defective condition of real property, and we overrule the Rogges’ second issue.3
Conclusion
We affirm the judgment of the trial court.
Justice Keyes, dissenting,
. In addition to the metal grate, the Rogges’ first amended petition also alleged that the holding cell itself and the toilet were "inadequate” and “defective” items of tangible personal property that had been supplied to their son. They further alleged that the City failed *575to provide him proper attire. None of these allegations have been relied upon by the Rogges on appeal to support their argument that they have pleaded a proper cause of action based on the City’s use of tangible personal property. Instead, their appellate arguments about waiver of immunity based on the alleged condition or use of tangible personal property are based solely on the alleged condition or use of the grate.
. See Appellants’ Br. at 24-28. Our dissenting colleague reformulates the Rogges’ arguments on appeal to emphasize the placement of the grate "directly over the toilet in the holding *578cell” as a critical aspect of the challenged condition of tangible personal property in this case. In fact, while the placement of the toilet is discussed in the factual background section of the Rogges’ brief to explain how the suicide occurred, the toilet is not referenced anywhere in the legal analysis. The placement of the grate over the toilet is particularly absent from the section of legal analysis arguing that the Rogges’ injuries "were caused by the condition of tangible personal property.” See id. Rather, in support of the argument that they pleaded facts sufficient to meet jurisdictional pleading requirements, the brief states simply: "The petition stated that Rogge was provided tangible personal property that was inadequate, defective and/or lacking an integral safety component, namely the grate in the holding cell that Rogge was placed in.” Id. at 26. The Rogges’ appellate argument did not rely bn the design of the jail cell or the relative placement of the toilet as an allegedly defective aspect of a condition of tangible personal property. Nor did it rely upon any alleged deprivation of depression medication. We do not consider arguments that were not urged on appeal. See, e.g., Bunton v. Bentley, 153 S.W.3d 50, 53 (Tex.2004) ("ordinarily, an appellant waives any complaint about the trial court’s judgment that is not raised in the court of appeals”). “ 'The premise of our adversarial system is that appellate courts do not sit as self-directed boards of legal inquiry and research, but essentially as arbiters of legal questions presented and argued by the parties before them.’ ” Nat'l Aeronautics & Space Admin. v. Nelson, 562 U.S. 134, 148 n.10, 131 S.Ct. 746, 757 n. 10, 178 L.Ed.2d 667 (2011) (Alito, J.) (quoting Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983) (Scalia, J.)).
. Based on our conclusion that governmental immunity has not been waived pursuant to the Tort Claims Act, Tex. Civ. Prac. & Rem. Code § 101.021(2), it is unnecessary for us to address the Rogges' third issue, which challenged the application of the statutory discretionary-function exception to waiver of immunity, id. § 101.056, argued by the City in the trial court. See Tex. R. Aré. P. 47.1.