Theorems · Theorem · general topology
IsPreirreducible.isPreconnected
∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α}, IsPreirreducible s → IsPreconnected s- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenproof · cited by 2,400
- IsPreconnectedstatement · cited by 205
- IsPreirreduciblestatement and proof · cited by 43
Cited by2
Results whose statement or proof uses this declaration.
- isPreconnected_emptyproof · cited by 14
- IsIrreducible.isConnectedproof · cited by 2