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.
Highlights
Quasiminimal distal function on a semitopological semigroup is introduced
We generalized the notion of distal flows and distal functions on an arbitrary semitopological semigroup S and studied their function spaces [3]
In the case of distal functions on a semigroup S, Junghenn has effectively used the universal mapping properties to show that the space of weakly almost periodic distal functions on S is the direct sum of the algebra of strongly almost periodic functions and two ideals of weakly almost "flight" functions on S [2]
Summary
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 study was an extension of Junghenn’s work on distal functions and their semigroup compactifications [2]. This approach of studying function spaces through semigroup compactifications enables one to take advantage of the universal mapping properties the compactifications enjoy. We introduce the quasiminimal distal function space QMD(S), and show that this space is an admissible C*osubalgebra of C(S).
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