Mathlib Map

Theorems · Theorem · general topology

SecondCountableTopology.is_open_generated_countable

∀ {α : Type u} {t : TopologicalSpace α} [self : SecondCountableTopology α],
  ∃ b, b.Countable ∧ t = TopologicalSpace.generateFrom b

There exists a countable set of sets that generates the topology.

Defined in
Mathlib.Topology.Bases
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
SecondCountableTopology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

TopologicalSpace.exists_countable_basis · cited by 9TopologicalSpace.exists_c…TopologicalSpace.secondCountableTopology_induced · cited by 1TopologicalSpace.secondCo…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSecondCountableTopology · cited by 750SecondCountableTopologySet.Countable · cited by 545Set.CountableTopologicalSpace.generateFrom · cited by 62TopologicalSpace.generate…SecondCountableTopology.is_op…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.