Mathlib Map

Theorems · Theorem · general topology

isClosedMap_snd_of_compactSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [CompactSpace X],
  IsClosedMap Prod.snd

If X is a compact topological space, then Prod.snd : X × Y → Y is a closed map.

Defined in
Mathlib.Topology.Maps.Proper.Basic
Cited by
1 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceCompactSpace
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Around this declaration

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

IsCompact.isClosed_image_restrict · cited by 1IsCompact.isClosed_image_…TopologicalSpace · cited by 24529TopologicalSpaceCompactSpace · cited by 593CompactSpaceIsClosedMap · cited by 138IsClosedMapIsProperMap.isClosedMap · cited by 14IsProperMap.isClosedMapisProperMap_snd_of_compactSpace · cited by 3isProperMap_snd_of_compac…isClosedMap_snd_of_compactSpa…CITED BYCITES

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Cited by1

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