Nice separation axioms

The epi-reflective hull B of an objectB in the category of locales is called anice separation axiom provided it enjoys certain properties which are natural generalizations of properties satisfied by the categories of completely regular locales and zero dimensional locales. Invariably, a family ofStone-like duality theorems ensues, distinguishing (for each large enough regular cardinal ) the full subcategory of all -LindelöfB-objects. Some corollaries for topological spaces arise, as well as some open problems, upon taking of spatial parts.This paper, consisting primarily of excerpts from the author's Ph.D. thesis, Wesleyan University, Middletown, Connecticut (1992), also represents, in part, the results of research engaged in at Charles University, Prague, during the 1992–1993 academic year, with the support of the United States Information Agency and the Fulbright Program.