Mathlib Map

Theorems · Theorem · general topology

IsProperMap.isClosed_range

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsProperMap f → IsClosed (Set.range f)

The range of a proper map is closed.

Defined in
Mathlib.Topology.Maps.Proper.Basic
Cited by
2 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

t2Space_of_properSMul_of_t1Group · cited by 0t2Space_of_properSMul_of_…t2Space_of_properVAdd_of_t1AddGroup · cited by 0t2Space_of_properVAdd_of_…TopologicalSpace · cited by 24529TopologicalSpaceSet.range · cited by 4705Set.rangeIsClosed · cited by 1639IsClosedIsProperMap · cited by 66IsProperMapIsProperMap.isClosedMap · cited by 14IsProperMap.isClosedMapIsClosedMap.isClosed_range · cited by 12IsClosedMap.isClosed_rangeIsProperMap.isClosed_rangeCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.