Theorems · Theorem · general topology
Homeomorph.image_symm
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y),
Set.image ⇑h.symm = Set.preimage ⇑h- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- Homeomorphstatement and proof · cited by 725
- Homeomorph.symmstatement and proof · cited by 365
- Homeomorph.toEquivproof · cited by 77
- Equiv.image_eq_preimage_symmproof · cited by 64
Cited by13
Results whose statement or proof uses this declaration.
- Homeomorph.isCompact_preimageproof · cited by 7
- MeasureTheory.Measure.toSphere_apply'proof · cited by 3
- Homeomorph.isPreconnected_imageproof · cited by 2
- IsEvenlyCovered.comp_homeomorphproof · cited by 2
- MeasureTheory.Measure.toSphere_apply_auxproof · cited by 2
- Homeomorph.image_connectedComponentInproof · cited by 1
- MeasureTheory.Measure.OuterRegular.mapproof · cited by 1
- Homeomorph.isPathConnected_preimageproof · cited by 0
- Homeomorph.isPreconnected_preimageproof · cited by 0
- Homeomorph.isSigmaCompact_preimageproof · cited by 0
- Homeomorph.isSimplyConnected_preimageproof · cited by 0
- intrinsicInterior_prod_eqproof · cited by 0