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Theorems · Theorem · general topology

IsClosedMap.domRestrict

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsClosedMap f → ∀ {s : Set X}, IsClosed s → IsClosedMap (s.domRestrict f)
Defined in
Mathlib.Topology.Constructions
Cited by
2 results in Mathlib
Foundations
Depth 72 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.

IsClosedMap.mapsToRestrict · cited by 0IsClosedMap.mapsToRestrictIsClosedMap.restrict · cited by 0IsClosedMap.restrictSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemIsClosed · cited by 1639IsClosedSet.domRestrict · cited by 383Set.domRestrictIsClosedMap · cited by 138IsClosedMapIsClosed.isClosedMap_subtype_val · cited by 8IsClosed.isClosedMap_subt…IsClosedMap.comp · cited by 6IsClosedMap.compIsClosedMap.domRestrictCITED BYCITES

Cites8

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Cited by2

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