Theorems · Definition · general topology
TopologicalSpace.countableBasis
(α : Type u) → [t : TopologicalSpace α] → [SecondCountableTopology α] → Set (Set α)
A countable topological basis of α.
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SecondCountableTopologystatement and proof · cited by 750
- TopologicalSpace.exists_countable_basisproof · cited by 9
Cited by14
Results whose statement or proof uses this declaration.
- TopologicalSpace.isBasis_countableBasisstatement · cited by 10
- TopologicalSpace.isOpen_iUnion_countableproof · cited by 9
- TopologicalSpace.countable_countableBasisstatement · cited by 8
- TopologicalSpace.isOpen_of_mem_countableBasisstatement and proof · cited by 4
- countable_setOfPred_covBy_rightproof · cited by 3
- countable_setOfPred_covBy_leftproof · cited by 2
- TopologicalSpace.IsTopologicalBasis.exists_countableproof · cited by 1
- TopologicalSpace.empty_notMem_countableBasisstatement · cited by 1
- TopologicalSpace.eq_generateFrom_countableBasisstatement · cited by 1
- ContinuousMap.secondCountableTopologyproof · cited by 0
- TopologicalSpace.nonempty_of_mem_countableBasisstatement and proof · cited by 0
- TopologicalSpace.countableBasis.congr_simpstatement and proof · cited by 0