Mappings to Realcompactifications

Document Type : Research Paper


Departemant of Mathematics, Shahid Chamran University, Ahvaz, Iran



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.
Using these, we provide different answers to the   four basic questions raised in Acharyya Finally, we give some notes on the realcompactifications  generated  by ideals.


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