Stone-breve{mbox{C}}ech compactifications derived from a discrete semigroup $S$ can be considered as a the spectrum of the algebra mathcal{B}(S)$ or as a collection of ultrafilters on S. What is certain and indisputable is the fact that filters play an important role in the study of Stone-breve{mbox{C}}$ech compactifications derived from a discrete semigroup.It seems that filters can play role in the study of general semigroup compactifications too. In the present paper, first we review the characterizations of semigroup in terms of filters and then some of the proposed results in cite{Talin1}- which set forth some characterizations of Stone-breve{mbox{C}}ech compactification- have been extended to a semigroup compactification derived from a Hausdorff semitopological semigroup.

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