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Theorems · Theorem · general topology

TopologicalSpace.IsTopologicalBasis.secondCountableTopology

∀ {α : Type u} [t : TopologicalSpace α] {b : Set (Set α)},
  TopologicalSpace.IsTopologicalBasis b → b.Countable → SecondCountableTopology α
Defined in
Mathlib.Topology.Bases
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
TopologicalSpace
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TopologicalSpace.secondCountableTopology_of_countable_cover · cited by 1TopologicalSpace.secondCo…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSecondCountableTopology · cited by 750SecondCountableTopologySet.Countable · cited by 545Set.CountableTopologicalSpace.IsTopologicalBasis · cited by 126TopologicalSpace.IsTopolo…TopologicalSpace.IsTopologicalBasis.eq_generateFrom · cited by 10IsTopologicalBasis.eq_gen…IsTopologicalBasis.secondCoun…CITED BYCITES

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