Theorems · Theorem · general topology
JoinedIn.map
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x y : X} {F : Set X},
JoinedIn F x y → ∀ {f : X → Y}, Continuous f → JoinedIn (f '' F) (f x) (f y)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.imagestatement · cited by 5,609
- Continuousstatement and proof · cited by 2,592
- Continuous.continuousOnproof · cited by 311
- JoinedInstatement and proof · cited by 40
- JoinedIn.map_continuousOnproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsInducing.joinedIn_imageproof · cited by 1
- IsPathConnected.invproof · cited by 0
- IsPathConnected.negproof · cited by 0