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Timeline for functional subrings

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Aug 28, 2012 at 20:21 comment added Ali Reza Dear Josh. Thank you very much for your notation. but it's better to see that in the study of rings of continuous functions, we could suppose that the topological space that all continuous functions defined on it, is completely regular Hausdorff space. then the case which you mentioned as an answer could not occur. As you Know for every topological space $X$ there exists a completely regular Hausdorff space $Y$ so that $C(X)$ and $C(Y)$ are ring isomorphic.
Aug 28, 2012 at 18:52 history answered Josh Ree CC BY-SA 3.0