Atlas home ||
Conferences |
Abstracts |
about Atlas
Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland |
|
Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis
View Abstracts
Conference Homepage |
Fractal dimensions vs. special sets of reals
by
Ondrej Zindulka
Czech Technical University
Recall that a set X ⊆ 2w is called
- null-additive if X+N is Lebesgue null for each Lebesgue null set
N ⊆ 2w,
- meager-additive if X+M is meager for each meager set
M ⊆ 2w,
- strongly null if X+M ≠ 2w for each meager set
M ⊆ 2w.
We characterize these three properties in terms
of Hausdorff and packing dimensions and use the characterization
to derive some results on the three classes, g-sets,
strong g-sets, Rothberger property etc.
The fractal geometry perspective is applied
to discusss the Scheepers Theorem that asserts that the
product of a strongly null set and a strongly null set with the
Hurewicz property is strongly null.
Date received: June 30, 2008
Copyright © 2008 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caxg-32.