TY - JOUR
T1 - Filters and the Weakly Almost Periodic Compactification of a Semitopological Semigroup
TT -
JF - IJMSI
JO - IJMSI
VL - 10
IS - 1
UR - http://ijmsi.ir/article-1-437-en.html
Y1 - 2015
SP - 59
EP - 80
KW - Semigroup compactification
KW - $Lmc$-compactification
KW - $wap$-compactification
KW - $z$-filter.
N2 - Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of the $wap-$compactification of a semitopological semigroup is constructed 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 $S^{Lmc}-S$.
M3 10.7508/ijmsi.2015.01.005
ER -