Connectedness, Homeomorphisms, & IVT – Lecture 19 (Topology)

A topological space X is called disconnected when:

1. A.There exist two open sets U, V with U ∪ V = X, U ∩ V = ∅, and neither U nor V is empty
2. B.Its only open sets are X and the empty set
3. C.Every singleton in X is an open set
4. D.There exists a continuous surjection from X onto ℝ