Theorems · Theorem · general topology
isConnected_singleton
∀ {α : Type u} [inst : TopologicalSpace α] {x : α}, IsConnected {x}- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsConnectedstatement · cited by 116
- isIrreducible_singletonproof · cited by 4
- IsIrreducible.isConnectedproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isPreconnected_singletonproof · cited by 3
- vadd_connectedComponentproof · cited by 1