Theorems · Theorem · general topology
t0Space_iff_ker_uniformity
∀ {α : Type u} [inst : UniformSpace α], T0Space α ↔ (uniformity α).ker = Set.diagonal α- Defined in
- Mathlib.Topology.UniformSpace.Separation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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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
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- T0Spacestatement · cited by 179
- Set.diagonalstatement and proof · cited by 42
- Filter.kerstatement and proof · cited by 40
- refl_mem_uniformityproof · cited by 15
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