Mathlib Map

Theorems · Theorem · general topology

IsClosedMap.of_nonempty

∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  (∀ (s : Set X), IsClosed s → s.Nonempty → IsClosed (f '' s)) → IsClosedMap f
Defined in
Mathlib.Topology.Maps.Basic
Cited by
2 results in Mathlib
Foundations
Depth 67 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.

isClosedMap_const · cited by 4isClosedMap_constValued.valuation_isClosedMap · cited by 1Valued.valuation_isClosed…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imageSet.Nonempty · cited by 2627Set.NonemptyIsClosed · cited by 1639IsClosedSet.eq_empty_or_nonempty · cited by 248Set.eq_empty_or_nonemptyIsClosedMap · cited by 138IsClosedMapSet.image_empty · cited by 73Set.image_emptyIsClosedMap.of_nonemptyCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.