Theorems · Theorem · algebraic topology
Homeomorph.isSimplyConnected_image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (f : X ≃ₜ Y) {s : Set X},
IsSimplyConnected (⇑f '' s) ↔ IsSimplyConnected s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.imagestatement · cited by 5,609
- Homeomorphstatement and proof · cited by 725
- Homeomorph.isEmbeddingproof · cited by 73
- IsSimplyConnectedstatement · cited by 13
- Topology.IsEmbedding.isSimplyConnected_imageproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- isSimplyConnected_smul_set_iffproof · cited by 1
- Homeomorph.isSimplyConnected_preimageproof · cited by 0
- isSimplyConnected_vadd_set_iffproof · cited by 0