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Let $S$ be a semitopological semigroup. The $wap-$ compactification ofsemigroup S, is a compact semitopological semigroup with certain universalproperties relative to the original semigroup, and the $Lmc-$ compactificationof semigroup $S$ is a universal semigroup compactification of $S$, which aredenoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internalconstruction of the $wap-$compactification of a semitopological semigroup isconstructed as a space of $z-$filters. Also we obtain the cardinality of$S^{wap}$ and show that if $S^{wap}$ is the one point compactification then$(S^{Lmc}-S)*S^{Lmc}$ is dense in $S^{Lmc}-S$.

Filters and the weakly almost periodic compactification of a semitopological semigroup