Mathlib Map

Theorems · Theorem · general topology

OpenPartialHomeomorph.IsImage.preimage_eq

∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  {e : OpenPartialHomeomorph X Y} {s : Set X} {t : Set Y}, e.IsImage s t → e.source ∩ ↑e ⁻¹' t = e.source ∩ s

Alias of the forward direction of OpenPartialHomeomorph.IsImage.iff_preimage_eq.

Defined in
Mathlib.Topology.OpenPartialHomeomorph.IsImage
Cited by
4 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OpenPartialHomeomorph.preimage_interior · cited by 1OpenPartialHomeomorph.pre…Bundle.Trivialization.frontier_preimage · cited by 0Trivialization.frontier_p…OpenPartialHomeomorph.preimage_closure · cited by 0OpenPartialHomeomorph.pre…OpenPartialHomeomorph.preimage_frontier · cited by 0OpenPartialHomeomorph.pre…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.preimage · cited by 4946Set.preimagePartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…OpenPartialHomeomorph.toFun' · cited by 745OpenPartialHomeomorph.toF…OpenPartialHomeomorph · cited by 664OpenPartialHomeomorphOpenPartialHomeomorph.IsImage · cited by 46OpenPartialHomeomorph.IsI…OpenPartialHomeomorph.IsImage.iff_preimage_eq · cited by 3IsImage.iff_preimage_eqIsImage.preimage_eqCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.