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Theorems · Theorem · general topology

local_compact_nhds

∀ {X : Type u_1} [inst : TopologicalSpace X] [LocallyCompactSpace X] {x : X} {n : Set X},
  n ∈ nhds x → ∃ s ∈ nhds x, s ⊆ n ∧ IsCompact s
Defined in
Mathlib.Topology.Compactness.LocallyCompact
Cited by
3 results in Mathlib
Foundations
Depth 51 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceLocallyCompactSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousMonoidHom.locallyCompactSpace_of_equicontinuousAt · cited by 1ContinuousMonoidHom.local…ContinuousAddMonoidHom.locallyCompactSpace_of_equicontinuousAt · cited by 1ContinuousAddMonoidHom.lo…IsOpenQuotientMap.locallyCompactSpace · cited by 0IsOpenQuotientMap.locally…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsIsCompact · cited by 1282IsCompactLocallyCompactSpace · cited by 324LocallyCompactSpaceLocallyCompactSpace.local_compact_nhds · cited by 6LocallyCompactSpace.local…local_compact_nhdsCITED BYCITES

Cites7

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Cited by3

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