Given a topological space \(X\). The space of continuous functions vanishing at infinity \(C_0(X)\) is a closed subspace of the space of bounded continuous function \(C^b(X)\).
Given a topological space \(X\). The space of continuous functions vanishing at infinity \(C_0(X)\) is a closed subspace of the space of bounded continuous function \(C^b(X)\).