Theorems · Theorem · general topology
nhds_le_nhdsSet_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X} {x : X}, nhds x ≤ nhdsSet s ↔ x ∈ s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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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
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- T1Spacestatement and proof · cited by 275
- nhdsSetstatement and proof · cited by 267
- Set.singleton_subset_iffproof · cited by 206
- nhdsSet_singletonproof · cited by 19
- nhdsSet_le_iffproof · cited by 2
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