Theorems · Theorem · general topology
TopologicalSpace.exists_seq_basis
∀ (α : Type u) [t : TopologicalSpace α] [SecondCountableTopology α], ∃ b, TopologicalSpace.IsTopologicalBasis (Set.range b)
- Defined in
- Mathlib.Topology.Bases
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangestatement and proof · cited by 4,705
- Set.Nonemptyproof · cited by 2,627
- IsEmptyproof · cited by 759
- SecondCountableTopologystatement and proof · cited by 750
- Set.Countableproof · cited by 545
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- Set.range_constproof · cited by 25
- Set.Countable.exists_eq_rangeproof · cited by 17
- TopologicalSpace.exists_countable_basisproof · cited by 9
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