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Theorems · Theorem · general topology

IsClosed.isCountablyCompact

∀ {E : Type u_2} [inst : TopologicalSpace E] {A : Set E} [CountablyCompactSpace E], IsClosed A → IsCountablyCompact A

A closed subset of a countably compact space is countably compact.

Defined in
Mathlib.Topology.Compactness.CountablyCompact
Cited by
0 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceCountablyCompactSpace
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Around this declaration

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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedSet.subset_univ · cited by 228Set.subset_univIsCountablyCompact · cited by 33IsCountablyCompactCountablyCompactSpace · cited by 7CountablyCompactSpaceCountablyCompactSpace.isCountablyCompact_univ · cited by 3CountablyCompactSpace.isC…IsCountablyCompact.of_isClosed_subset · cited by 1IsCountablyCompact.of_isC…IsClosed.isCountablyCompactCITED BYCITES

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