Theorems · Theorem · general topology
JoinedIn.refl
∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X} {F : Set X}, x ∈ F → JoinedIn F x x- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 3 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.
Cites6
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
- JoinedInstatement · cited by 40
- Path.reflproof · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- mem_pathComponentIn_selfproof · cited by 7
- Set.Countable.isPathConnected_compl_of_one_lt_rankproof · cited by 2
- isPathConnected_singletonproof · cited by 1