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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