Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777814 | Topology and its Applications | 2017 | 10 Pages |
Abstract
A classical theorem of Malykhin says that if {Xα:αâ¤Îº} is a family of compact spaces such that t(Xα)â¤Îº, for every αâ¤Îº, then t(âαâ¤ÎºXα)â¤Îº, where t(X) is the tightness of a space X. In this paper we prove the following counterpart of Malykhin's theorem for functional tightness: Let {Xα:α<λ} be a family of compact spaces such that t0(Xα)â¤Îº for every α<λ. If λâ¤2κ or λ is less than the first measurable cardinal, then t0(âα<λXα)â¤Îº, where t0(X) is the functional tightness of a space X. In particular, if there are no measurable cardinals, then the functional tightness is preserved by arbitrarily large products of compacta. Our result answers a question posed by Okunev.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
MikoÅaj Krupski,