ABSTRACT
Topology is a branch of mathematics that studies the properties of geometric objects which remain unaltered under \deformation." The idea of deformation involves strongly the notion of continuity. The notions of continuity of functions and convergence of sequences are the two most fundamental concepts in analysis. Both the concepts are based on the abstraction of our intuitive sense of closeness of points of a set. For example, the usual - denition for continuity of real or complex valued functions on the real line R1 (or the complex plane C) and the denition of convergence of sequences in these spaces are based on this idea. \Closeness" of elements of a set can be measured most conveniently as distance between the elements. In any set endowed with a suitable notion of distance, one can dene convergence of sequences and talk about continuity of functions between such sets. Maurice Frechet (1906), perhaps motivated by this observation, introduced \metric spaces."
