Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications

Abstract

\begin{abstrac} Let $(X,T)$ be a topological space, and ${}^{\ast }X$ a non--standard extension of $X$. There is a natural ``standard'' topology ${}^{S}T$ on ${}^{\ast }X$ generated by ${}^{\ast }G$, where $G\in T$. The topological space ${(}^{\ast }X{,}^{S}T)$ will be used to study compactifications of $(X,T)$ in a systematic way.

5 pages