Theorems · Theorem · general topology
t2_separation_nhds
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {x y : X},
x ≠ y → ∃ u v, u ∈ nhds x ∧ v ∈ nhds y ∧ Disjoint u v- Defined in
- Mathlib.Topology.Separation.Hausdorff
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 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.
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 · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- IsOpenproof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- T2Spacestatement and proof · cited by 1,351
- IsOpen.mem_nhdsproof · cited by 470
- t2_separationproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- ProperlyDiscontinuousSMul.exists_nhds_image_smul_eq_selfproof · cited by 3
- ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_selfproof · cited by 3