Theorems · Theorem · general topology
Homeomorph.apply_symm_apply
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) (y : Y),
h (h.symm y) = y- 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.apply_symm_applyproof · cited by 346
- Homeomorph.toEquivproof · cited by 77
Cited by18
Results whose statement or proof uses this declaration.
- Homeomorph.comap_nhds_eqproof · cited by 23
- Homeomorph.self_comp_symmproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- TopCat.I.homeomorph_oneproof · cited by 2
- TopCat.I.homeomorph_zeroproof · cited by 2
- IsCoveringMapOn.homeomorph_compproof · cited by 2
- IsEvenlyCovered.toTrivialization_applyproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symmproof · cited by 1
- Homeomorph.symm_trans_selfproof · cited by 1
- IsEvenlyCovered.comp_subtypeValproof · cited by 1
- IsEvenlyCovered.restrictPreimageproof · cited by 1
- IsCoveringMap.comp_homeomorph_iffproof · cited by 0