Theorems · Theorem · general topology
OpenPartialHomeomorph.map_nhds_eq
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) {x : X}, x ∈ e.source → Filter.map (↑e) (nhds x) = nhds (↑e x)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- le_antisymmproof · cited by 2,068
- PartialEquiv.sourcestatement and proof · cited by 964
- PartialHomeomorph.toPartialEquivstatement and proof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement and proof · cited by 851
- Filter.mapstatement · cited by 819
- OpenPartialHomeomorph.toFun'statement · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- OpenPartialHomeomorph.continuousAtproof · cited by 23
Cited by7
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.map_extend_nhdsproof · cited by 6
- HasStrictFDerivAt.map_nhds_eq_of_equivproof · cited by 5
- IsLocalHomeomorphOn.map_nhds_eqproof · cited by 2
- Bundle.Trivialization.map_proj_nhdsproof · cited by 2
- OpenPartialHomeomorph.symm_map_nhds_eqproof · cited by 2
- OpenPartialHomeomorph.eventually_nhdsproof · cited by 2
- OpenPartialHomeomorph.image_mem_nhdsproof · cited by 1