Theorems · Theorem · general topology
Homeomorph.isOpen_image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) {s : Set X},
IsOpen (⇑h '' s) ↔ IsOpen s- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement · cited by 5,609
- IsOpenstatement and proof · cited by 2,400
- Homeomorphstatement and proof · cited by 725
- Homeomorph.symmproof · cited by 365
- Homeomorph.preimage_symmproof · cited by 9
- Homeomorph.isOpen_preimageproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Homeomorph.isOpenMapproof · cited by 30
- IsEvenlyCovered.homeomorph_compproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- Algebra.quasiFiniteAt_iff_isOpen_singleton_fiberproof · cited by 1
- extremallyDisconnected_of_homeoproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iffproof · cited by 1
- Algebra.QuasiFiniteAt.of_isOpen_singleton_fiberproof · cited by 1