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Theorems · Theorem · general topology

IsOpenQuotientMap.of_comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Y} {g : Y → Z},
  Continuous f → Function.Surjective f → Continuous g → IsOpenQuotientMap (g ∘ f) → IsOpenQuotientMap g
Defined in
Mathlib.Topology.Maps.OpenQuotient
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsOpenQuotientMap.of_comp_iff · cited by 0IsOpenQuotientMap.of_comp…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousIsOpenQuotientMap · cited by 65IsOpenQuotientMapFunction.Surjective.of_comp · cited by 30Surjective.of_compIsOpenQuotientMap.isOpenMap · cited by 16IsOpenQuotientMap.isOpenM…IsOpenQuotientMap.surjective · cited by 16IsOpenQuotientMap.surject…IsOpenMap.of_comp · cited by 2IsOpenMap.of_compIsOpenQuotientMap.of_compCITED BYCITES

Cites7

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Cited by1

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