Theorems · Inductive type · general topology
WeaklyLocallyCompactSpace
(X : Type u_3) → [TopologicalSpace X] → Prop
We say that a topological space is a weakly locally compact space, if each point of this space admits a compact neighborhood.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by38
Results whose statement or proof uses this declaration.
- WeaklyLocallyCompactSpace.exists_compact_mem_nhdsstatement and proof · cited by 28
- FiniteDimensional.of_locallyCompactSpacestatement and proof · cited by 7
- exists_compact_supersetstatement and proof · cited by 6
- IsCompact.locallyCompactSpace_of_mem_nhds_of_addGroupproof · cited by 5
- refinement_of_locallyCompact_sigmaCompact_of_nhds_basis_setstatement and proof · cited by 3
- MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_lestatement and proof · cited by 3
- exists_mem_nhds_isCompact_isClosedstatement and proof · cited by 2
- IsCompact.locallyCompactSpace_of_mem_nhds_of_groupproof · cited by 2
- MeasureTheory.measure_univ_of_isAddLeftInvariantstatement and proof · cited by 2
- MeasureTheory.Content.outerMeasure_lt_top_of_isCompactstatement and proof · cited by 2
- Metric.exists_isCompact_closedBallstatement and proof · cited by 2
- RestrictedProduct.weaklyLocallyCompactSpace_of_principalstatement and proof · cited by 1