Compact Topological Semigroups Associated with Oids


Abdol Mohammad Aminpour - Department of Mathematical Sciences and Computer, Shahid Chamran University, Ahvaz, Iran. Mehrdad Seilani - Iranian Academic Center for Education Culture and Research(ACECR).


The known theory for a discrete oid \(T\) shows that how to find a subset \(T^{\infty}\) of \(\beta T\) which is a compact right topological semigroup (see section 2 for details).In this paper we try to find an analogue of almost periodic functions for oids. We discover, new compact semigroups by using a certain subspace of functions \(u^{\infty}(T)\) of \(C(T)\) for an oid \(T\) for which \(f\beta\) is continuous on \(T^{\infty}\times(T\cup T^{\infty}\cup TT^{\infty})\),where \((T\cup T^{\infty}\cup TT^{\infty})\) is a suitable subspace of \(\beta T\) for a wide range.