Theorems · Theorem · general topology
RegularSpace.of_exists_mem_nhds_isClosed_subset
∀ {X : Type u_1} [inst : TopologicalSpace X],
(∀ (x : X), ∀ s ∈ nhds x, ∃ t ∈ nhds x, IsClosed t ∧ t ⊆ s) → RegularSpace X- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites12
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Disjointproof · cited by 2,201
- IsClosedstatement and proof · cited by 1,639
- closureproof · cited by 1,254
- nhdsSetproof · cited by 267
- List.TFAE.outproof · cited by 177
- Filter.lift'proof · cited by 99
- RegularSpacestatement and proof · cited by 63
- regularSpace_TFAEproof · cited by 6
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