Theorems · Theorem · general topology
Homeomorph.injective
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y),
Function.Injective ⇑h- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 14 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.
Cites5
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
- Equiv.injectiveproof · cited by 464
- Homeomorph.toEquivproof · cited by 77
Cited by14
Results whose statement or proof uses this declaration.
- Homeomorph.isEmbeddingproof · cited by 73
- Homeomorph.isProperMapproof · cited by 6
- TopCat.I.extproof · cited by 3
- IsEvenlyCovered.toTrivialization_applyproof · cited by 1
- SpectrumRestricts.starAlgHom_injectiveproof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- Homeomorph.comap_coclosedCompactproof · cited by 1
- exists_homeomorph_image_eqproof · cited by 1
- Ideal.exists_not_mem_forall_mem_of_ne_of_liesOverproof · cited by 1
- isQuotientCoveringMap_iff_isCoveringMap_andproof · cited by 0
- Topology.IsEmbedding.toHomeomorph_symm_applyproof · cited by 0
- Topology.IsCoinducing.connectedComponentsHomeomorph_symm_mk_applyproof · cited by 0