Theorems · Theorem · general topology

Topology.IsClosedEmbedding.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},
  Topology.IsClosedEmbedding f → Topology.IsClosedEmbedding g → Topology.IsClosedEmbedding (Prod.map f g)

Defined in: Mathlib.Topology.Constructions.SumProd
Cited by: 1 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace TopologicalSpace

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Cites8

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

TopologicalSpacestatement and proof · cited by 24,529
Topology.IsEmbeddingproof · cited by 294
Topology.IsClosedEmbeddingstatement and proof · cited by 195
Topology.IsClosedEmbedding.isClosed_rangeproof · cited by 41
Topology.IsClosedEmbedding.isEmbeddingproof · cited by 25
Set.range_prodMapproof · cited by 19
IsClosed.prodproof · cited by 10
Topology.IsEmbedding.prodMapproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

Topology.IsClosedEmbedding.units_mapproof · cited by 1