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Theorems · Theorem · general topology

IsDenseInducing.separableSpace

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β}
  [TopologicalSpace.SeparableSpace α], IsDenseInducing i → TopologicalSpace.SeparableSpace β

If the domain of a IsDenseInducing map is a separable space, then so is the codomain.

Defined in
Mathlib.Topology.DenseEmbedding
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace.SeparableSpace
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Around this declaration

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IsDenseEmbedding.separableSpace · cited by 0IsDenseEmbedding.separabl…TopologicalSpace · cited by 24529TopologicalSpaceTopologicalSpace.SeparableSpace · cited by 109TopologicalSpace.Separabl…IsDenseInducing · cited by 56IsDenseInducingIsDenseInducing.dense · cited by 20IsDenseInducing.denseIsDenseInducing.continuous · cited by 4IsDenseInducing.continuousDenseRange.separableSpace · cited by 2DenseRange.separableSpaceIsDenseInducing.separableSpaceCITED BYCITES

Cites6

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Cited by1

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