Theorems · Theorem · general topology
TopologicalSpace.IsTopologicalBasis.eq_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [T0Space X] {b : Set (Set X)},
TopologicalSpace.IsTopologicalBasis b → ∀ {x y : X}, x = y ↔ ∀ s ∈ b, x ∈ s ↔ y ∈ s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT0Space
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Cites6
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
- T0Spacestatement and proof · cited by 179
- TopologicalSpace.IsTopologicalBasisstatement and proof · cited by 126
- inseparable_iff_eqproof · cited by 3
- TopologicalSpace.IsTopologicalBasis.inseparable_iffproof · cited by 1
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