The regularity series of a convergence space

Abstract

The regularity series, or brieflyR-series, of a convergence space is an ordinal sequence of spaces leading to the regular modification of the space. The behavior of this series is studied relative to such basic constructs as products, subspaces, and various quotient maps. Upper bounds on the length of theR-series are obtained for several classes of spaces. This series can be employed to construct regular completions and compactifications.