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Theorems · Theorem · general topology

IsDenseInducing.prodMap

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] [inst_3 : TopologicalSpace δ] {e₁ : α → β} {e₂ : γ → δ},
  IsDenseInducing e₁ → IsDenseInducing e₂ → IsDenseInducing (Prod.map e₁ e₂)

The product of two dense inducings is a dense inducing

Defined in
Mathlib.Topology.DenseEmbedding
Cited by
4 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace
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Around this declaration

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

UniformSpace.Completion.coe_mul · cited by 6Completion.coe_mulIsDenseInducing.extend_Z_bilin · cited by 1IsDenseInducing.extend_Z_…UniformSpace.Completion.inner_coe · cited by 1Completion.inner_coeIsDenseEmbedding.prodMap · cited by 0IsDenseEmbedding.prodMapTopologicalSpace · cited by 24529TopologicalSpaceTopology.IsInducing · cited by 266Topology.IsInducingIsDenseInducing · cited by 56IsDenseInducingIsDenseInducing.dense · cited by 20IsDenseInducing.denseIsDenseInducing.isInducing · cited by 9IsDenseInducing.isInducingTopology.IsInducing.prodMap · cited by 7IsInducing.prodMapDenseRange.prodMap · cited by 5DenseRange.prodMapIsDenseInducing.prodMapCITED BYCITES

Cites7

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Cited by4

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