Theorems · Theorem · general topology
exists_continuous_nonneg_pos
∀ {X : Type u_1} [inst : TopologicalSpace X] [RegularSpace X] [LocallyCompactSpace X] (x : X),
∃ f, HasCompactSupport ⇑f ∧ 0 ≤ ⇑f ∧ f x ≠ 0- Defined in
- Mathlib.Topology.UrysohnsLemma
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- ContinuousMapstatement and proof · cited by 2,491
- Set.Iccproof · cited by 1,702
- IsCompactproof · cited by 1,282
- Set.EqOnproof · cited by 603
- LocallyCompactSpacestatement and proof · cited by 324
- HasCompactSupportstatement and proof · cited by 196
- mem_of_mem_nhdsproof · cited by 126
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarScalarFactor_eq_mulproof · cited by 6
- MeasureTheory.Measure.addModularCharacterFun_eq_addHaarScalarFactorproof · cited by 3
- MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactorproof · cited by 3
- MeasureTheory.Measure.addHaarScalarFactor_domSMulproof · cited by 3
- MeasureTheory.Measure.addHaarScalarFactor_selfproof · cited by 3
- MeasureTheory.Measure.haarScalarFactor_eq_mulproof · cited by 3
- MeasureTheory.Measure.haarScalarFactor_selfproof · cited by 3
- MeasureTheory.Measure.haarScalarFactor_smulproof · cited by 1
- MeasureTheory.Measure.mul_addHaarScalarFactor_smulproof · cited by 1
- MeasureTheory.Measure.mul_haarScalarFactor_smulproof · cited by 1