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Theorems · Theorem · general topology

exists_positiveCompacts_subset

∀ {α : Type u_1} [inst : TopologicalSpace α] [LocallyCompactSpace α] {U : Set α}, IsOpen U → U.Nonempty → ∃ K, ↑K ⊆ U
Defined in
Mathlib.Topology.Sets.Compacts
Cited by
1 results in Mathlib
Foundations
Depth 61 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.

IsOpen.exists_positiveCompacts_closure_subset · cited by 0IsOpen.exists_positiveCom…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSetLike.coe · cited by 8199SetLike.coeSet.Nonempty · cited by 2627Set.NonemptyIsOpen · cited by 2400IsOpenIsCompact · cited by 1282IsCompactinterior · cited by 714interiorLocallyCompactSpace · cited by 324LocallyCompactSpaceTopologicalSpace.PositiveCompacts · cited by 112TopologicalSpace.Positive…exists_compact_subset · cited by 4exists_compact_subsetexists_positiveCompacts_subsetCITED BYCITES

Cites10

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Cited by1

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