# The Banach–Mazur game and σ-porosity

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 3, page 197-210
- ISSN: 0016-2736

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topZelený, Miroslav. "The Banach–Mazur game and σ-porosity." Fundamenta Mathematicae 150.3 (1996): 197-210. <http://eudml.org/doc/212171>.

@article{Zelený1996,

abstract = {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.},

author = {Zelený, Miroslav},

journal = {Fundamenta Mathematicae},

keywords = {proper sequence; -porosity; metric space; uniformly porous sets; Banach-Mazur game},

language = {eng},

number = {3},

pages = {197-210},

title = {The Banach–Mazur game and σ-porosity},

url = {http://eudml.org/doc/212171},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Zelený, Miroslav

TI - The Banach–Mazur game and σ-porosity

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 3

SP - 197

EP - 210

AB - 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.

LA - eng

KW - proper sequence; -porosity; metric space; uniformly porous sets; Banach-Mazur game

UR - http://eudml.org/doc/212171

ER -

## References

top- [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. Zbl0435.28011
- [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.

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