5 papers
Homeomorphisms between compact subsets of real numbers
Sławomir Kusiński, Szymon Plewik
We first present a reduction of properties of compact sets of real numbers to properties of countable orders. Then discuss a variant of homogeneity of compact subsets of real numbe…
On the methods of reduction of some types of Marczewski-Burstin measurable functions to continuous functions on products of perfect sets
Waldemar Hołubowski, Sławomir Kusiński
In this paper, we introduce product-wise generalizations of certain Marczewski-Burstin bases, including sets with the (s)-property and completely Ramsey sets. For each of these fam…
Application of fusion technique to the solution of Harrington problem and its generalizations to Baire functions, part I
Sławomir Kusiński
In this paper we provide solutions of the Harrington problem (along with a few generalizations) proposed in a book Analytic Sets. The original problem asks if for arbitrary sequenc…
Connections between Kuratowski partitions of Baire spaces, measurable cardinals and precipitous ideals
Sławomir Kusiński
In this paper we present a few properties of -partitions, which are partitions of Baire spaces such that all subfamilies of such a partition sum to a set with the Baire property…
A simple, combinatorial proof of Gowers Dichotomy for Banach Spaces
Ryszard Frankiewicz, Sławomir Kusiński
In this paper we present a simple proof of Gowers Dichotomy which states that every infinite dimensional Banach Space has a subspace which either contains an unconditional basic se…