Theorems · Theorem · algebraic topology
IsSimplyConnected.isPathConnected
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsSimplyConnected s → IsPathConnected s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- IsPathConnectedstatement · cited by 65
- SimplyConnectedSpaceproof · cited by 19
- IsSimplyConnectedstatement and proof · cited by 13
- isPathConnected_iff_pathConnectedSpaceproof · cited by 4
- IsSimplyConnected.simplyConnectedSpaceproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsSimplyConnected.nonemptyproof · cited by 1