Additivity properties of topological diagonalizations
                    
                        
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منابع مشابه
Additivity properties of topological diagonalizations
In a work of Just, Miller, Scheepers and Szeptycki it was asked whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions. In a recent work, Scheepers proved that one of the properties in question is closed under taking countable unions. After surveying the known results, we show that none of the remaining classes is prov...
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The Hausdorff dimension of a product X × Y can be strictly greater than that of Y , even when the Hausdorff dimension of X is zero. But when X is countable, the Hausdorff dimensions of Y and X × Y are the same. Diagonalizations of covers define a natural hierarchy of properties which are weaker than “being countable” and stronger than “having Hausdorff dimension zero”. Fremlin asked whether it ...
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We consider the question, which of the major classes defined by topological diagonalizations of open or Borel covers is provably, or at least consistently, hereditary. Many of the classes in the open case are not hereditary already in ZFC. We show that none of them is provably hereditary. This is contrasted with the Borel case, where some of the classes are provably hereditary. We also give two...
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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 properti...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2003
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1067620185