Let X , Y , Z be non empty topological spaces, let F be a continuous map from X into Y , and let G be a continuous map from Y into Z . Then G F is a continuous map from X into Z . Let X , Y be non empty topological spaces, let W be a point of Y , let A be a continuous map from X into Y , and let G be a neighbourhood of W . Let X be a non empty topological space, A , B be subsets of the carrier of X , and U 1 be a neighbourhood of B . If A B , then U 1 is a neighbourhood of A .
B is compact.