Topologies and Cotopologies Generated by Sets of Functions
Melvin Henriksen · 2020
In what follows, the readers will be given a preview of some joint research efforts by R. Kopperman, and R. G. Woods whose central theme is concerned with describing conditions. They apply this mainly, but not exclusively to the study of subspaces of F-spaces and to spaces of minimal prime ideals of certain kinds of commutative rings. This chapter determines to what extent it is possible to derive properties of topological spaces from the existence of bases derived from special collections of functions with values. The fact that the techniques apply also to subspaces of F-spaces may be regarded as both a bonus and a way of showing that some of the conditions on bases are not strong enough to characterize spaces of minimal prime ideals of uniformly closed rings of continuous functions. The chapter applies the theory to give simpler proofs of known results and to derive new results about the class of spaces just described.