QUASIMINIMAL DISTAL FUNCTION SPACE AND ITS SEMIGROUP COMPACTIFICATION

ABSTRACT. Quasiminimal distal function on a semitopological semigroup is introduced. The concept of right topological semigroup compactification is employed to study the algebra of quasiminimal distal functions. The universal mapping property of the quasiminimal distal compactification is obtained. KEY WORDS AND PHRASES. Quasiminimal distal flows and distal functions, right topological semigroup compactification, universal mapping property. 1980 AMS SUBJECT CLASSIFICATION CODES. Primary 43A60, 22A20 secondary 43A07 In a recent paper, we generalized the notion of distal flows and distal functions on an arbitrary semitopological semigroup S and studied their function spaces [3]. The study was an extension of Junghenn’s work on distal functions and their semigroup compactifications [2]. The impetus for the author’s work in this area is the study by Berglund et al. in which the authors have introduced several kinds of function spaces which are admissible C*-subalgebras of C(S) and studied these function spaces through semigroup compactifications [i]. Interestingly, these compactifications possess certain universal mapping properties, universa