Theorems · Theorem · general topology
T0Space.of_open_cover
∀ {X : Type u_1} [inst : TopologicalSpace X], (∀ (x : X), ∃ s, x ∈ s ∧ IsOpen s ∧ T0Space ↑s) → T0Space X- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites8
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.Elemstatement and proof · cited by 7,166
- IsOpenstatement and proof · cited by 2,400
- T0Spacestatement and proof · cited by 179
- Inseparableproof · cited by 160
- Inseparable.mem_open_iffproof · cited by 11
- T0Space.of_coverproof · cited by 1
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