Theorems · Theorem · general topology
Topology.IsEmbedding.toHomeomorph_symm_apply
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
(hf : Topology.IsEmbedding f) (x : X), hf.toHomeomorph.symm ⟨f x, ⋯⟩ = x- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Homeomorphstatement · cited by 725
- Homeomorph.symmstatement and proof · cited by 365
- Topology.IsEmbeddingstatement and proof · cited by 294
- Homeomorph.apply_symm_applyproof · cited by 18
- Topology.IsEmbedding.toHomeomorphstatement and proof · cited by 16
- Homeomorph.injectiveproof · cited by 14
- Topology.IsEmbedding.toHomeomorph_apply_coeproof · cited by 1
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