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[Merged by Bors] - chore: rename OpenPartialHomeomorph.to_isOpenEmbedding #41854

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[Merged by Bors] - chore: rename OpenPartialHomeomorph.to_isOpenEmbedding #41854

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2 changes: 1 addition & 1 deletion Mathlib/Geometry/Manifold/Instances/Sphere.lean
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Expand Up @@ -307,7 +307,7 @@ theorem range_stereographic_symm (hv : ‖v‖ = 1) (hv' : v ∈ sphere 0 1 := b

lemma isOpenEmbedding_stereographic_symm (hv : ‖v‖ = 1) :
Topology.IsOpenEmbedding (stereographic hv).symm :=
(stereographic hv).symm.to_isOpenEmbedding (by simp)
(stereographic hv).symm.isOpenEmbedding (by simp)

end StereographicProjection

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10 changes: 6 additions & 4 deletions Mathlib/Topology/OpenPartialHomeomorph/Basic.lean
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Expand Up @@ -15,8 +15,8 @@ public import Mathlib.Topology.Sets.Opens
## Main definitions

* `OpenPartialHomeomorph.refl`: the identity open partial homeomorphism
* `Topology.IsOpenEmbedding.toOpenPartialHomeomorph`: construct a partial homeomorphism from an
open embedding
* `Topology.IsOpenEmbedding.toOpenPartialHomeomorph`: construct an open partial homeomorphism from
an open embedding
-/

@[expose] public section
Expand Down Expand Up @@ -224,10 +224,12 @@ theorem isOpenEmbedding_restrict : IsOpenEmbedding (e.source.restrict e) := by

/-- 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`. -/
theorem to_isOpenEmbedding (h : e.source = Set.univ) : IsOpenEmbedding e :=
theorem isOpenEmbedding (h : e.source = Set.univ) : IsOpenEmbedding e :=
e.isOpenEmbedding_restrict.comp
((Homeomorph.setCongr h).trans <| Homeomorph.Set.univ X).symm.isOpenEmbedding

@[deprecated (since := "2026-07-17")] alias to_isOpenEmbedding := isOpenEmbedding

end OpenPartialHomeomorph

/-!
Expand All @@ -239,7 +241,7 @@ variable (f : X → Y) (h : IsOpenEmbedding f)

/-- An open embedding of `X` into `Y`, with `X` nonempty, defines an open partial homeomorphism
whose source is all of `X`. The converse is also true; see
`OpenPartialHomeomorph.to_isOpenEmbedding`. -/
`OpenPartialHomeomorph.isOpenEmbedding`. -/
@[simps! (attr := mfld_simps) -fullyApplied apply source target]
noncomputable def toOpenPartialHomeomorph [Nonempty X] : OpenPartialHomeomorph X Y :=
OpenPartialHomeomorph.ofContinuousOpen (h.isEmbedding.injective.injOn.toPartialEquiv f univ)
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