Theorems · Theorem · general topology
TopologicalSpace.isTopologicalBasis_empty
∀ {α : Type u} [t : TopologicalSpace α], TopologicalSpace.IsTopologicalBasis ∅ ↔ IsEmpty α- Defined in
- Mathlib.Topology.Bases
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites9
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.univproof · cited by 3,945
- IsEmptystatement and proof · cited by 759
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- TopologicalSpace.generateFromproof · cited by 62
- Set.sUnion_emptyproof · cited by 17
- Set.univ_eq_empty_iffproof · cited by 13
- TopologicalSpace.IsTopologicalBasis.sUnion_eqproof · cited by 4
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