Covariant and contravariant approaches to topology (Q1380734)

Summary: In [Topology Appl. 74, No. 1-3, 225-258 (1996; Zbl 0869.54038)] the author presented certain results of basic topology from the point of view of Extension Theory. In [the author, Covariant and contravariant points of view in topology with applications to function spaces, Preprint 1997] the approach of the paper cited above is broadened. This paper is an exposition of results contained in the 1997 preprint. Its purpose is to present a way of viewing 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.