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Keywords:
essential weak ideal; weak socle; minimal ideal; almost discrete space; scattered space; Stone-Čech compactification; realcompactification
essential weak ideal; weak socle; minimal ideal; almost discrete space; scattered space; Stone-Čech compactification; realcompactification
Summary:
Let $C(X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C(X)$. The intersection of essential weak ideal in $C(X)$ is also studied.
References:
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