Theorems · Inductive type · general topology
PreconnectedSpace
(α : Type u) → [TopologicalSpace α] → Prop
A preconnected space is one where there is no non-trivial open partition.
- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by69
Results whose statement or proof uses this declaration.
- PreconnectedSpace.isPreconnected_univstatement and proof · cited by 26
- MeromorphicOn.exists_meromorphicOrderAt_ne_top_iff_forallproof · cited by 7
- isClopen_iffstatement and proof · cited by 6
- intermediate_value_univ₂statement and proof · cited by 5
- IsClopen.eq_univstatement and proof · cited by 5
- AddTorsor.connectedSpacestatement and proof · cited by 4
- isPreconnected_iff_preconnectedSpacestatement and proof · cited by 4
- IsSeparatedMap.eq_of_comp_eqstatement and proof · cited by 4
- Subtype.preconnectedSpacestatement · cited by 4
- preconnectedSpace_iff_clopenstatement and proof · cited by 3
- ConnectedSpace.casesOnstatement and proof · cited by 2
- subsingleton_of_disjoint_isClopenstatement and proof · cited by 2