Theorems · Theorem · general topology

OpenPartialHomeomorph.isOpenEmbedding

∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  (e : OpenPartialHomeomorph X Y), e.source = Set.univ → Topology.IsOpenEmbedding ↑e

An open partial homeomorphism whose source is all of X defines an open embedding of X into Y. The converse is also true; see IsOpenEmbedding.toOpenPartialHomeomorph.

Defined in

Mathlib.Topology.OpenPartialHomeomorph.Basic

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace