Theorems · Theorem · general topology
Homeomorph.comap_nhds_eq
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) (y : Y),
Filter.comap (⇑h) (nhds y) = nhds (h.symm y)- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 23 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 and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Homeomorphstatement and proof · cited by 725
- Filter.comapstatement and proof · cited by 546
- Homeomorph.symmstatement and proof · cited by 365
- Homeomorph.apply_symm_applyproof · cited by 18
- Homeomorph.nhds_eq_comapproof · cited by 4
Cited by23
Results whose statement or proof uses this declaration.
- nhds_translation_add_negproof · cited by 5
- nhds_translation_mul_invproof · cited by 4
- comap_mulLeft_nhdsGT_zeroproof · cited by 1
- nhds_translation_mul_inv₀proof · cited by 1
- DomMulAct.comap_mk.symm_nhdsproof · cited by 0
- MulOpposite.comap_op_leftUniformSpaceproof · cited by 0
- DomAddAct.comap_mk_nhdsproof · cited by 0
- nhds_one_symmproof · cited by 0
- DomAddAct.comap_mk.symm_nhdsproof · cited by 0
- AddOpposite.comap_unop_nhdsproof · cited by 0
- comap_inv_leftUniformSpaceproof · cited by 0
- comap_neg_leftUniformSpaceproof · cited by 0