Regularity and Sequential Convergence Spaces

Abstract

ABSTRACT. Regularity for sequential convergence spaces is defined, and two reasons for believing that it is the right definition are given. In the first place, the definition is equivalent to an “extension of maps” property that characterizes regularity in a variety of topological categories. Second, a sequential convergence space is regular (in the sense here) iff its γ‐modification (introduced by Beattie and Butzmann) is a regular (filter) convergence space.