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Theorems · Theorem · general topology

isOpenMap_snd

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y], IsOpenMap Prod.snd

The second projection in a product of topological spaces sends open sets to open sets.

Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
3 results in Mathlib
Foundations
Depth 76 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.

isOpenQuotientMap_snd · cited by 2isOpenQuotientMap_sndisOpen_prod_iff' · cited by 0isOpen_prod_iff'isOpenMap_prodMap_iff · cited by 0isOpenMap_prodMap_iffTopologicalSpace · cited by 24529TopologicalSpaceEq.ge · cited by 375Eq.geIsOpenMap · cited by 253IsOpenMapisOpenMap_iff_nhds_le · cited by 6isOpenMap_iff_nhds_lemap_snd_nhds · cited by 1map_snd_nhdsisOpenMap_sndCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.