Mappings to Realcompactifications

Abstract

In this paper, we introduce and study a mapping from the collection of all intermediate rings of $C(X)$ to the collection of all realcompactifications of $X$ contained in $beta X$. By establishing the relations between this mapping and its converse, we give a different approach to the main statements of De et. al. <br />Using these, we provide different answers to the four basic questions raised in Acharyya et.al. Finally, we give some notes on the realcompactifications generated by ideals.