Theorems · Theorem · general topology
TopologicalSpace.nonempty_of_mem_countableBasis
∀ {α : Type u} [t : TopologicalSpace α] [inst : SecondCountableTopology α] {s : Set α},
s ∈ TopologicalSpace.countableBasis α → s.Nonempty- Defined in
- Mathlib.Topology.Bases
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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.Nonemptystatement · cited by 2,627
- SecondCountableTopologystatement and proof · cited by 750
- Set.nonempty_iff_ne_emptyproof · cited by 96
- TopologicalSpace.countableBasisstatement and proof · cited by 14
- TopologicalSpace.empty_notMem_countableBasisproof · cited by 1
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