Theorems · Theorem · general topology

OpenPartialHomeomorph.to_isOpenEmbedding

Deprecated since 2026-07-17Use OpenPartialHomeomorph.isOpenEmbedding instead.

∀ {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

Alias of OpenPartialHomeomorph.isOpenEmbedding. 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

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace