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C ( X ) can sometimes determine X without X being realcompact

Melvin HenriksenBiswajit Mitra — 2005

Commentationes Mathematicae Universitatis Carolinae

As usual C ( X ) will denote the ring of real-valued continuous functions on a Tychonoff space X . It is well-known that if X and Y are realcompact spaces such that C ( X ) and C ( Y ) are isomorphic, then X and Y are homeomorphic; that is C ( X ) X . The restriction to realcompact spaces stems from the fact that C ( X ) and C ( υ X ) are isomorphic, where υ X is the (Hewitt) realcompactification of X . In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact...

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