|
چکیده
|
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.
|