Mappings to Realcompactifications

author

Mehdi Parsinia Departemant of Mathematics, Shahid Chamran University, Ahvaz, Iran

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. 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.

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Journal title

Categories and General Algebraic Structures with Application

volume 10 issue 1

pages 107- 116

publication date 2019-01-01

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Keywords

Realcompacification intermediate ring intermediate $C$-ring

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