Theorems · Theorem · general topology

t2_separation

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] {x y : X},
  x ≠ y → ∃ u v, IsOpen u ∧ IsOpen v ∧ x ∈ u ∧ y ∈ v ∧ Disjoint u v

Two different points can be separated by open sets.

Defined in

Mathlib.Topology.Separation.Hausdorff

Cited by

11 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2Space