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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 |
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Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis
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Applications of the Kuratowski-Ulam theorem
by
Szymon Plewik
Instytut Matematyki, Uniwersytet Śląski, Katowice, Poland
The Kuratowski-Ulam theorem was applied three times:
- Each tower is universally measure zero and always of first category.
See, Sz. Plewik,
Towers are universally measure zero and always of first category,
PAMS 119 (1993) 865 - 868.
- The covering number for meager sets of the real line equals to the covering number for meager sets of the plane equipped with a C-cross topology, whenever the family C contains a p-base for the product topology. See,
A. Kucharski and Sz. Plewik,
Cardinal invariants for C-cross topologies,
Note di Matematica, vol. 27, suppl. n.1 (2007), 97 - 106.
- The Kuratowski-Ulam theorem holds for the product of two topological spaces, whenever the second factor is I-favorable. See, A. Kucharski, Sz. Plewik, Game approach to universally Kuratowski–Ulam spaces, Topology Appl. 154 (2) (2007) 421–427.
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-33.