On a class of pseudocompact spaces derived from ring epimorphisms
نویسنده
چکیده
A Tychonoff space X is called RG if the embedding of C(X) → C(Xδ) is an epimorphism of rings. Compact RG spaces are known and easily described. We study the pseudocompact RG spaces. These must be scattered of finite Cantor Bendixon degree but need not be locally compact. However, under strong hypotheses, (countable compactness, or small cardinality) these spaces must, indeed, be compact. The main theorem shows, how to construct a suitable maximal almost disjoint family, and apply it to obtain examples of RG spaces that are almost compact, locally compact, non-compact, and of Cantor Bendixon degree 2. More complicated examples ensue. AMS classification: 54C30. ∗Supported by GAČR 201/03/0933 and PAPIIT grant IN108802-2, Mexico. †Supported by the NSERC of Canada. ‡Supported by the NSERC of Canada.
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