Theorems · Theorem · general topology
joinedIn_iff_joined
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {F : Set X} (x_in : x ∈ F) (y_in : y ∈ F),
JoinedIn F x y ↔ Joined ⟨x, x_in⟩ ⟨y, y_in⟩- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- unitIntervalproof · cited by 607
- continuous_subtype_valproof · cited by 159
- JoinedInstatement and proof · cited by 40
- Joinedstatement and proof · cited by 29
- Path.mapproof · cited by 21
- Joined.somePathproof · cited by 12
- Path.map_coeproof · cited by 6
- JoinedIn.joined_subtypeproof · cited by 1
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