Theorems · Theorem · general topology
OpenPartialHomeomorph.mapsTo
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y), Set.MapsTo (↑e) e.source e.target- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement · cited by 851
- OpenPartialHomeomorph.toFun'statement · cited by 745
- Set.MapsTostatement · cited by 732
- OpenPartialHomeomorphstatement and proof · cited by 664
- PartialEquiv.targetstatement · cited by 650
- OpenPartialHomeomorph.map_sourceproof · cited by 21
Cited by15
Results whose statement or proof uses this declaration.
- differentiableWithinAt_localInvariantPropproof · cited by 13
- OpenPartialHomeomorph.mapsTo_symmproof · cited by 5
- writtenInExtChartAt_mapsToproof · cited by 1
- StructureGroupoid.LocalInvariantProp.left_invarianceproof · cited by 1
- OpenPartialHomeomorph.preimage_eventuallyEq_target_inter_preimage_interproof · cited by 1
- OpenPartialHomeomorph.source_preimage_targetproof · cited by 1
- StructureGroupoid.LocalInvariantProp.right_invarianceproof · cited by 1
- OpenPartialHomeomorph.bijOnproof · cited by 1
- contDiffWithinAt_localInvariantProp_of_leproof · cited by 1
- OpenPartialHomeomorph.eventually_nhdsWithinproof · cited by 1