Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Weiss, Tomasz"'
We provide new techniques to construct sets of reals without perfect subsets and with the Hurewicz or Menger covering properties. In particular, we show that if the Continuum Hypothesis holds, then there are such sets which can be mapped continuously
Externí odkaz:
http://arxiv.org/abs/2406.12609
Autor:
Weiss, Tomasz, Zakrzewski, Piotr
We study a strengthening of the notion of a universally meager set and its dual counterpart that strengthens the notion of a universally null set. We say that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager (respectively, cou
Externí odkaz:
http://arxiv.org/abs/2304.07579
Autor:
Szewczak, Piotr, Weiss, Tomasz
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set into the Cantor cube are null-additive, it contains a homeomorphic co
Externí odkaz:
http://arxiv.org/abs/2006.10796
Autor:
Weiss, Tomasz, Zakrzewski, Piotr
Publikováno v:
In Annals of Pure and Applied Logic January 2024 175(1) Part A
Autor:
Korch, Michał, Weiss, Tomasz
In this paper, we are interested in parallels to the classical notions of special subsets in $\R$ defined in the generalized Cantor and Baire spaces ($2^\kappa$ and $\kappa^\kappa$). We consider generalizations of the well-known classes of special su
Externí odkaz:
http://arxiv.org/abs/1802.05750
Autor:
Korch, Michał, Weiss, Tomasz
Publikováno v:
Bulletin Polish Acad. Sci. Math. 64 (2016) , 1-20
We introduce two new classes of special subsets of the real line: the class of perfectly null sets and the class of sets which are perfectly null in the transitive sense. These classes may play the role of duals to the corresponding classes on the ca
Externí odkaz:
http://arxiv.org/abs/1609.04005
Autor:
Tsaban, Boaz, Weiss, Tomasz
Publikováno v:
Real Analysis Exchange 30 (2004/5), 819--836
We describe a simple machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: 1. The product of a meager/null-additive set and a strong measure zero/strong
Externí odkaz:
http://arxiv.org/abs/math/0307226
Autor:
Weiss, Tomasz, Tsaban, Boaz
Publikováno v:
Note di Matematica 22 (2003), 83--92
The Hausdorff dimension of a product XxY 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 XxY are the same. Diagonalizations of covers define a natural
Externí odkaz:
http://arxiv.org/abs/math/0212009
The paper contains two results pointing to the lack of symmetry between measure and category. Assume CH. There exists a strongly meager subset of the Cantor set that can be mapped onto the Cantor set by a uniformly continuous function. (It is well kn
Externí odkaz:
http://arxiv.org/abs/math/0111284