Theorems · Theorem · general topology
Homeomorph.preimage_frontier
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) (s : Set Y),
⇑h ⁻¹' frontier s = frontier (⇑h ⁻¹' s)- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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.preimagestatement · cited by 4,946
- Homeomorphstatement and proof · cited by 725
- frontierstatement · cited by 214
- Homeomorph.continuousproof · cited by 53
- Homeomorph.isOpenMapproof · cited by 30
- IsOpenMap.preimage_frontier_eq_frontier_preimageproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Complex.frontier_reProdImproof · cited by 3
- NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTopproof · cited by 1
- Homeomorph.image_frontierproof · cited by 1