The Banach–Mazur game and σ-porosity

• Autorzy: Miroslav Zelený
• Języki publikacji: EN

Abstrakty

EN

It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 26E99: None of the above, but in this section
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 150
• Numer: 3
• Strony: 197-210

Daty

wydano

1996

otrzymano

1993-11-09

poprawiono

1996-01-25

Twórcy

autor

Miroslav Zelený

• KMA, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 186 00, Czech Republic

Bibliografia

• [D] E. P. Dolzhenko, Boundary properties of arbitrary functions, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 3-14 (in Russian).
• [K] A. S. Kechris, Classical Descriptive Set Theory, Springer, 1995.
• [O] J. C. Oxtoby, Measure and Category, Springer, 1980.
• [Z1] L. Zajíček, On differentiability properties of Lipschitz functions on a Banach space with a uniformly Gateaux differentiable bump function, preprint, 1995.
• [Z2] L. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (1987-88), 314-350.