Theorems · Theorem · general topology
mem_pathComponent_of_mem
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X}, x ∈ pathComponent y → y ∈ pathComponent x- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- pathComponentstatement and proof · cited by 30
- Joined.symmproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- pathComponent_symmproof · cited by 1