An introduction to topology and its applications: A new approach

Abstract

The present paper aims to introduce the topic of topology to a reader with little background knowledge of university mathematics. Unlike the traditional approach which begins by abstracting of real analysis to metric spaces and then routing to topological spaces, our present exposition of opology exploits some basic experience with computations, scientific measurements and observations, such as those encountered in the use of a scientific calculator, a computer program or a measuring device. It is hoped that, in the present age of computers and information technology, topology, which is known to be an abstract mathematical subject, can be made palatable and relevant to a wider audience. Conjugate to our main discourse, we introduce some necessary knowledge of functional programming which is needed by the reader to understand how applications of topology can be realized in a concrete manner.