Theorems · Theorem · general topology
Continuous.connectedComponentsLift_continuous
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
[inst_2 : TotallyDisconnectedSpace β] {f : α → β} (h : Continuous f), Continuous h.connectedComponentsLift- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- TotallyDisconnectedSpacestatement and proof · cited by 295
- ConnectedComponentsstatement · cited by 40
- Continuous.connectedComponentsLiftstatement · cited by 4
- Continuous.quotient_liftOn'proof · cited by 3
- Continuous.image_eq_of_connectedComponent_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Continuous.connectedComponentsMap_continuousproof · cited by 0