Let B be a subset of a metric space (X1, d1). The set B is said to be disconnected if there exist disjoint open subsets U and V such that A set B is connected if it is not disconnected. Let (X 2 , d 2...

Let B be a subset of a metric space (X1, d1). The set B is said to be disconnected if there exist disjoint open subsets U and V such that

A set B is connected if it is not disconnected. Let (X₂, d₂) be a metric space and suppose f : X₁
→ X₂
is continuous. Prove that if B is a connected subset of X₁, then f (B ) is a connected subset of X₂. That is, the continuous image of a connected set is connected.