Theorems · Theorem · general topology

separated_by_isOpenEmbedding

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

Defined in

Mathlib.Topology.Separation.Hausdorff

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2Space