Theorems · Theorem · general topology
connectedSpace_iff_univ
∀ {α : Type u} [inst : TopologicalSpace α], ConnectedSpace α ↔ IsConnected Set.univ- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
- Assumes
- TopologicalSpace
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
- Set.univstatement and proof · cited by 3,945
- IsConnectedstatement and proof · cited by 116
- Set.Nonempty.someproof · cited by 53
- ConnectedSpacestatement and proof · cited by 37
- PreconnectedSpace.isPreconnected_univproof · cited by 26
- Set.univ_nonemptyproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Function.Surjective.connectedSpaceproof · cited by 1
- connectedSpace_iff_clopenproof · cited by 0