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Theorems · Theorem · general topology

isCountablyCompact_iff_countablyCompactSpace

∀ {E : Type u_2} [inst : TopologicalSpace E] {A : Set E}, IsCountablyCompact A ↔ CountablyCompactSpace ↑A
Defined in
Mathlib.Topology.Compactness.CountablyCompact
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

IsCountablyCompact.isSeqCompact · cited by 1IsCountablyCompact.isSeqC…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemIsCountablyCompact · cited by 33IsCountablyCompactCountablyCompactSpace · cited by 7CountablyCompactSpaceisCountablyCompact_iff_isCountablyCompact_univ · cited by 1isCountablyCompact_iff_is…isCountablyCompact_univ_iff · cited by 1isCountablyCompact_univ_i…isCountablyCompact_iff_counta…CITED BYCITES

Cites7

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Cited by1

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