Theorems · Theorem · general topology
Subtype.connectedSpace
∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α}, IsConnected s → ConnectedSpace ↑s- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 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.
Cites10
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.Elemstatement and proof · cited by 7,166
- IsConnectedstatement and proof · cited by 116
- PreconnectedSpaceproof · cited by 64
- Set.Nonempty.to_subtypeproof · cited by 55
- ConnectedSpacestatement · cited by 37
- IsConnected.isPreconnectedproof · cited by 36
- IsConnected.nonemptyproof · cited by 18
- Subtype.preconnectedSpaceproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- isConnected_iff_connectedSpaceproof · cited by 7
- AnalyticOnNhd.exists_analyticOrderAt_ne_top_iff_forallproof · cited by 1