مهرداد کاروان جهرمی

For a Tychonoff space $X$‎, ‎say $X^*=\beta X\setminus X$ denotes‎ ‎the reminder of $X$ in its Stone-Check compactification $\beta X$‎. ‎About a half century ago‎, ‎Fynne and gilman introduced the notion of remote point‎, ‎i.e‎. ‎a point $p\in ‎X^*‎$ which is not‎ ‎a limit point (in $\beta X$) of a nowhere dense subset in $X$‎. ‎Remote points ‎and some close notions such as $\omega-$far points‎, ‎lonely points and‎ weakly P-points play a main role to ‎distinguish between spaces whose remainders are homogeneous and whose which are not‎. ‎This thesis mainly devotes for investigation about remote points and some‎ ‎other close notions‎. ‎It is shown that every non pseudocompact $ccc-$space with $\pi$-weight $\omega_1$ has remote point and (under $\mathrm{CH}$) the real line‎ ‎has remote point‎. ‎Using notions $\omega-$far points‎, ‎lonely points‎, ‎it is shown that $\omega^*$ is not homogeneous‎.