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Theorems · Theorem · general topology

Subtype.isCountablyCompact_iff

∀ {E : Type u_2} [inst : TopologicalSpace E] {p : E → Prop} {A : Set { x // p x }},
  IsCountablyCompact A ↔ IsCountablyCompact (Subtype.val '' A)
Defined in
Mathlib.Topology.Compactness.CountablyCompact
Cited by
1 results in Mathlib
Foundations
Depth 78 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_iff_isCountablyCompact_univ · cited by 1isCountablyCompact_iff_is…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imageTopology.IsEmbedding.subtypeVal · cited by 41IsEmbedding.subtypeValIsCountablyCompact · cited by 33IsCountablyCompactTopology.IsEmbedding.isCountablyCompact_iff · cited by 1IsEmbedding.isCountablyCo…Subtype.isCountablyCompact_iffCITED BYCITES

Cites6

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Cited by1

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