Abstract
0. Introduction. Let X be a topological space, and denote by C(X) the set of all real-valued continuous functions defined on X, by C*(X) the subset of C(X) composed of bounded functions. Both C(X) and C*(X) can be considered as a ring under pointwise addition and multiplication of functions, or as a semigroup under pointwise multiplication. For a completely regular Hausdorff space X, let f ix and vX denote the (~ech Stone compactification and the Hewitt realcompactification of X, respectively (see e. g. [2]). The following propositions are well-known for completely regular Hausdortf spaces X and Y:
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