can sometimes determine without being realcompact
As usual will denote the ring of real-valued continuous functions on a Tychonoff space . It is well-known that if and are realcompact spaces such that and are isomorphic, then and are homeomorphic; that is . The restriction to realcompact spaces stems from the fact that and are isomorphic, where is the (Hewitt) realcompactification of . In this note, a class of locally compact spaces that includes properly the class of locally compact realcompact...