Theorems · Theorem · general topology
PathConnectedSpace.exists_path_through_family
∀ {X : Type u_1} [inst : TopologicalSpace X] [PathConnectedSpace X] {n : ℕ} (p : Fin (n + 1) → X),
∃ γ, ∀ (i : Fin (n + 1)), p i ∈ Set.range ⇑γ- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Set.univproof · cited by 3,945
- unitIntervalstatement · cited by 607
- Pathstatement and proof · cited by 318
- IsPathConnectedproof · cited by 65
- PathConnectedSpacestatement and proof · cited by 26
- pathConnectedSpace_iff_univproof · cited by 7
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