International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 621-626

Covariant and contravariant approaches to topology

Jerzy Dydak

Department of Mathematics, University of Tennessee, Knoxville 37996, Tennessee, USA

Received 22 April 1997; Revised 12 June 1997

Copyright © 1997 Jerzy Dydak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is an exposition of results contained in [2]. The purpose of [2] is to present a way of viewing of basic topology which unifies quite a few results and concepts previously seemed not related (quotient maps, product topology, subspace topology, separation axioms, topologies on function spaces, dimension, metrizability). The basic idea is that in order to investigate an unknown space X, one either maps known spaces to X or maps X to known spaces.