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Theorems · Theorem · general topology

IsDenseEmbedding.separableSpace

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

If the domain of a IsDenseEmbedding is a separable space, then so is its codomain.

Defined in
Mathlib.Topology.DenseEmbedding
Cited by
0 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace.SeparableSpace
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TopologicalSpace · cited by 24529TopologicalSpaceTopologicalSpace.SeparableSpace · cited by 109TopologicalSpace.Separabl…IsDenseEmbedding · cited by 24IsDenseEmbeddingIsDenseEmbedding.isDenseInducing · cited by 6IsDenseEmbedding.isDenseI…IsDenseInducing.separableSpace · cited by 1IsDenseInducing.separable…IsDenseEmbedding.separableSpa…CITED BYCITES

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