Y be topological spaces, V be a subset of X , and W be a subset of Y . Let X , Y be topological spaces, V be a subset of the carrier of X , and W be a subset of the carrier of Y . Let x be a point of X , y be a point of Y , V be a neighbourhood of x , and W be a neighbourhood of y . Let A be a subset of the carrier of X , B be a subset of the carrier of Y , V be a neighbourhood of A , and W be a neighbourhood of B . Let X , Y be non empty topological spaces.
C be a set.
C be a set. Suppose D is open. Let X 1 be a subset of X and Y 1 be a subset of Y . Let X , Y be sets, let f be a function from 2 X into 2 Y , and let R be a family of subsets of X . Then f R is a family of subsets of Y .