Theorems · Theorem · general topology
Homeomorph.map_nhds_eq
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) (x : X),
Filter.map (⇑h) (nhds x) = nhds (h x)- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 72 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 · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.mapstatement · cited by 819
- Homeomorphstatement and proof · cited by 725
- Homeomorph.isEmbeddingproof · cited by 73
- EquivLike.range_eq_univproof · cited by 27
- Topology.IsEmbedding.map_nhds_of_memproof · cited by 2
Cited by31
Results whose statement or proof uses this declaration.
- Homeomorph.symm_map_nhds_eqproof · cited by 3
- map_add_left_nhdsproof · cited by 3
- map_add_right_nhdsproof · cited by 2
- AffineSpace.asymptoticNhds_smulproof · cited by 2
- map_mul_left_nhdsproof · cited by 2
- map_mul_right_nhdsproof · cited by 2
- IsTopologicalGroup.isOpenMap_iff_nhds_oneproof · cited by 1
- nhds_one_symm'proof · cited by 1
- nhds_smulproof · cited by 1
- ContinuousLinearEquiv.map_nhds_eqproof · cited by 1
- nhds_zero_symm'proof · cited by 1
- map_mul_left_nhds₀proof · cited by 1