Theorems · Theorem · general topology
IsLocalHomeomorph.localInverseAt_apply_self
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
(hf : IsLocalHomeomorph f) {x : X}, ↑(hf.localInverseAt x) (f x) = xThe function localInverseAt x sends f x back to x.
- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- OpenPartialHomeomorph.toFun'statement and proof · cited by 745
- IsLocalHomeomorphstatement and proof · cited by 35
- IsLocalHomeomorph.localInverseAtstatement and proof · cited by 7
- IsLocalHomeomorph.self_mem_localInverseAt_targetproof · cited by 2
- IsLocalHomeomorph.injOn_localInverseAt_targetproof · cited by 1
- IsLocalHomeomorph.apply_localInverseAt_of_memproof · cited by 1
- IsLocalHomeomorph.apply_self_mem_localInverseAt_sourceproof · cited by 1
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