Mathlib Map

Theorems · Theorem · general topology

isProperMap_of_isClosedMap_of_inj

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Continuous f → Function.Injective f → IsClosedMap f → IsProperMap f

An injective continuous and closed map is proper.

Defined in
Mathlib.Topology.Maps.Proper.Basic
Cited by
3 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

Topology.IsClosedEmbedding.isProperMap · cited by 6IsClosedEmbedding.isPrope…Homeomorph.isProperMap · cited by 6Homeomorph.isProperMapIsHomeomorph.isProperMap · cited by 1IsHomeomorph.isProperMapTopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousIsClosedMap · cited by 138IsClosedMapIsProperMap · cited by 66IsProperMapisProperMap_iff_isClosedMap_of_inj · cited by 1isProperMap_iff_isClosedM…isProperMap_of_isClosedMap_of…CITED BYCITES

Cites5

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Cited by3

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