ABSTRACT
The continuity of functions between topological spaces is the central notion in topology. The conditions of a topological structure have been so formulated that the denition of a continuous function can be borrowed word for word from analysis. The rst section is devoted to the discussion of this concept. We will also study here the notion of equivalence for topological spaces, and related concepts. The second section of this chapter concerns the construction of new topological spaces out of old ones. We have already studied such a method, namely, Relativization. Given an indexed family of topological spaces, we can construct their \cartesian product." We shall go into a method of topologising this set, in a natural and useful way.
