Additivity Numbers of Covering Properties
نویسنده
چکیده
The additivity number of a topological property (relative to a given space) is the minimal number of subspaces with this property whose union does not have the property. The most well-known case is where this number is greater than א0, i.e. the property is σ-additive. We give a rather complete survey of the known results about the additivity numbers of a variety of topological covering properties, including those appearing in the Scheepers diagram (which contains, among others, the classical properties of Menger, Hurewicz, Rothberger, and Gerlits-Nagy). Some of the results proved here were not published beforehand, and many open problems are posed.
منابع مشابه
2 8 Ju n 20 09 LINEAR σ - ADDITIVITY AND SOME APPLICATIONS
We show that a large family of well-studied covering properties, which are not necessarily σ-additive, are preserved by countable increasing unions. Using this and simple forcing theoretic methods, we explain several phenomena, settle some problems, and construct topological groups with very strong combinatorial properties.
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