Theorems · Theorem · general topology

IsPreconnected.inter_derivedSet_nonempty

∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {U : Set X},
  IsPreconnected U →
    ∀ (a b : Set X),
      U ⊆ a ∪ b →
        (U ∩ derivedSet a).Nonempty → (U ∩ derivedSet b).Nonempty → (U ∩ (derivedSet a ∩ derivedSet b)).Nonempty

Defined in

Mathlib.Topology.DerivedSet

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT1Space