On κ-bounded and M-compact reflections of topological spaces

Abstract

For a topological space X its reflection in a class T of topological spaces is a pair (TX,iX) consisting of a space TX∈T and a continuous map iX:X→TX such that for any continuous map f:X→Y to a space Y∈T there exists a unique continuous map f¯:TX→Y such that f=f¯∘iX. In this paper for an infinite cardinal κ and a nonempty set M of ultrafilters on κ, we study the reflections of topological spaces in the classes Hκ of κ-bounded Hausdorff spaces and HM of M-compact Hausdorff spaces (a topological space X is κ-bounded if the closures of subsets of cardinality ≤κ in X are compact; X is M-compact if any function x:κ→X has a p-limit in X for every ultrafilter p∈M).