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The structure of the σideal of σporous sets
, 1999
"... We show a general method of construction of nonσporous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each nonσporous Suslin subset of a topologically complete metric space contains a nonσporous closed subset. We show also a sufficie ..."
Abstract

Cited by 6 (2 self)
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We show a general method of construction of nonσporous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each nonσporous Suslin subset of a topologically complete metric space contains a nonσporous closed subset. We show also a sufficient condition, which gives that a certain system of compact sets contains a nonσporous element. Namely, if we denote the space of all compact subsets of a compact metric space E with the Hausdorff metric by K(E), then it is shown that each analytic subset of K(E) containing all countable compact subsets of E contains necessarily an element, which is nonσporous subset of E. We show several applications of this result to problems from real and harmonic analysis (e.g. the existence of a closed nonσporous set of uniqueness for trigonometric series). Finally we investigate also descriptive properties of the σideal of compact σporous sets.
Trichotomies for ideals of compact sets
 J. SYMBOLIC LOGIC
"... We prove several trichotomy results for ideals of compact sets. Typically, we show that a “sufficiently rich” universally Baire ideal is either Π 0 3hard, or Σ 0 3hard, or else a σideal. ..."
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Cited by 5 (3 self)
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We prove several trichotomy results for ideals of compact sets. Typically, we show that a “sufficiently rich” universally Baire ideal is either Π 0 3hard, or Σ 0 3hard, or else a σideal.