Theorems · Theorem · general topology

nonempty_inter

∀ {α : Type u} [inst : TopologicalSpace α] [PreconnectedSpace α] {s t : Set α},
  IsOpen s → IsOpen t → s ∪ t = Set.univ → s.Nonempty → t.Nonempty → (s ∩ t).Nonempty

Defined in

Mathlib.Topology.Connected.Clopen

Cited by

2 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpacePreconnectedSpace