Theorems · Theorem · general topology
Homeomorph.symm_apply_apply
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) (x : X),
h.symm (h x) = x- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Homeomorphstatement and proof · cited by 725
- Homeomorph.symmstatement · cited by 365
- Equiv.symm_apply_applyproof · cited by 320
- Homeomorph.toEquivproof · cited by 77
Cited by18
Results whose statement or proof uses this declaration.
- Homeomorph.symm_comp_selfproof · cited by 5
- Homeomorph.symm_map_nhds_eqproof · cited by 3
- ContinuousMap.exists_extensionproof · cited by 2
- Algebra.quasiFiniteAt_iff_isOpen_singleton_fiberproof · cited by 1
- TopCat.stdSimplexHomeomorphI_symm_oneproof · cited by 1
- TopCat.stdSimplexHomeomorphI_symm_zeroproof · cited by 1
- isEmbedding_of_iSup_eq_top_of_preimage_subset_rangeproof · cited by 1
- Homeomorph.self_trans_symmproof · cited by 1
- Ideal.exists_not_mem_forall_mem_of_ne_of_liesOverproof · cited by 1
- MeasureTheory.locallyIntegrable_map_homeomorphproof · cited by 1
- IsEvenlyCovered.restrictPreimageproof · cited by 1
- Algebra.QuasiFiniteAt.of_isOpen_singleton_fiberproof · cited by 1