Theorems · Theorem · general topology
Specializes.joinedIn
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {F : Set X}, x ⤳ y → x ∈ F → y ∈ F → JoinedIn F x y- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 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.
Cites12
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
- unitIntervalproof · cited by 607
- continuous_constproof · cited by 278
- Specializesstatement and proof · cited by 176
- Set.piecewiseproof · cited by 136
- isClosed_singletonproof · cited by 66
- Set.piecewise_eq_of_memproof · cited by 49
- Set.piecewise_eq_of_notMemproof · cited by 49
- JoinedInstatement · cited by 40
- IsClosed.continuous_piecewise_of_specializesproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsInducing.joinedIn_imageproof · cited by 1
- Inseparable.joinedInproof · cited by 0