Mathlib Map

Theorems · Theorem · general topology

IsOpenQuotientMap.prodMap

∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : X → Y} {g : Z → W},
  IsOpenQuotientMap f → IsOpenQuotientMap g → IsOpenQuotientMap (Prod.map f g)
Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
4 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsModuleTopology.isQuotientMap_of_surjectiveₛₗ · cited by 3IsModuleTopology.isQuotie…SeparationQuotient.isQuotientMap_prodMap_mk · cited by 0SeparationQuotient.isQuot…t2Space_iff_of_isOpenQuotientMap · cited by 0t2Space_iff_of_isOpenQuot…QuotientRing.isQuotientMap_coe_coe · cited by 0QuotientRing.isQuotientMa…TopologicalSpace · cited by 24529TopologicalSpaceIsOpenQuotientMap · cited by 65IsOpenQuotientMapContinuous.prodMap · cited by 28Continuous.prodMapIsOpenQuotientMap.isOpenMap · cited by 16IsOpenQuotientMap.isOpenM…IsOpenQuotientMap.surjective · cited by 16IsOpenQuotientMap.surject…IsOpenQuotientMap.continuous · cited by 15IsOpenQuotientMap.continu…Function.Surjective.prodMap · cited by 8Surjective.prodMapIsOpenMap.prodMap · cited by 6IsOpenMap.prodMapIsOpenQuotientMap.prodMapCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.