Theorems · Theorem · general topology

separated_by_continuous

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T2Space Y] {f : X → Y},
  Continuous f → ∀ {x y : X}, f x ≠ f y → ∃ u v, IsOpen u ∧ IsOpen v ∧ x ∈ u ∧ y ∈ v ∧ Disjoint u v

Defined in

Mathlib.Topology.Separation.Hausdorff

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2Space