Covariant and contravariant approaches to topology

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.