Theorems · Theorem · general topology

isPreconnected_closed_iff

∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α},
  IsPreconnected s ↔
    ∀ (t t' : Set α),
      IsClosed t → IsClosed t' → s ⊆ t ∪ t' → (s ∩ t).Nonempty → (s ∩ t').Nonempty → (s ∩ (t ∩ t')).Nonempty

Defined in

Mathlib.Topology.Connected.Basic

Cited by

6 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace