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Theorems · Theorem · general topology

Topology.IsEmbedding.secondCountableTopology

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {f : α → β} [inst_1 : TopologicalSpace β]
  [SecondCountableTopology β], Topology.IsEmbedding f → SecondCountableTopology α
Defined in
Mathlib.Topology.Bases
Cited by
6 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceSecondCountableTopology
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Around this declaration

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

TopologicalSpace.IsSeparable.secondCountableTopology · cited by 4IsSeparable.secondCountab…Topology.IsClosedEmbedding.polishSpace · cited by 2IsClosedEmbedding.polishS…ModelWithCorners.secondCountableTopology · cited by 2ModelWithCorners.secondCo…Topology.IsEmbedding.separableSpace · cited by 0IsEmbedding.separableSpaceTopologicalSpace.NonemptyCompacts.secondCountableTopology_iff · cited by 0NonemptyCompacts.secondCo…TopologicalSpace.Compacts.secondCountableTopology_iff · cited by 0Compacts.secondCountableT…TopologicalSpace · cited by 24529TopologicalSpaceSecondCountableTopology · cited by 750SecondCountableTopologyTopology.IsEmbedding · cited by 294Topology.IsEmbeddingTopology.IsEmbedding.toIsInducing · cited by 48IsEmbedding.toIsInducingTopology.IsInducing.secondCountableTopology · cited by 3IsInducing.secondCountabl…IsEmbedding.secondCountableTo…CITED BYCITES

Cites5

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Cited by6

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