Authors: | Bell, Murray Ginsburg, John Todorčević, Stevo |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Countable spread of exp Y and λY | Journal: | Topology and its Applications | Volume: | 14 | Issue: | 1 | First page: | 1 | Last page: | 12 | Issue Date: | 1-Jan-1982 | ISSN: | 0166-8641 | DOI: | 10.1016/0166-8641(82)90043-8 | Abstract: | We show that it is consistent with ZFC that there exists a compact 0-dimensional Hausdorff space X for which exp X has countable spread, but X is not metrizable. This establishes the independence of Malyhin's problem. The space X also has no uncountable weakly separated subspaces, its superextension is first countable, and its square is a strong S-space. For 0-dimensional Y we prove that λY has countable spread iff Y is compact and metrizable. We show that it is consistent with ZFC that if Y is 0-dimensional and λY is first countable, then Y is compact and metrizable. |
Publisher: | Elsevier |
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