in this paper we establish a characterization of abelian compact hausdorff semigroups with unique idempotent and ideal retraction property. we also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

Erdal Ekici has introduced and studied nearly continuous multifunctions [Acta Math. Univ. Comenianae, Vol. LXXII, 2 (2003), pp. 1–7]. The purpose of the present paper is to introduce and study upper and lower almost nearly continuous multifunctions as a weaker form of upper and lower nearly continuous multifunctions. Basic characterizations, several properties of upper and lower almost nearly c...

It is the objective of this paper to introduce a new class of generalizations of continuous functions via λ-open sets called weakly λcontinuous functions. Moreover, we study some of its fundamental properties. It turns out that weak λ-continuity is weaker than λ-continuity [1]. AMS Mathematics Subject Classification (2000): 54C10, 54D10