Theorems · Theorem · general topology
eq_of_nhds_neBot
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {x y : X}, (nhds x ⊓ nhds y).NeBot → x = y- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- T2Spacestatement and proof · cited by 1,351
- Filter.NeBotstatement and proof · cited by 853
- t2_iff_nhdsproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCompact.isClosedproof · cited by 77
- UniformSpace.Completion.continuous_hatInvproof · cited by 1