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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Functions equivalent to Borel measurable ones

Komisarski A., Michalewski H., Milewski P.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 1

55-64

Let X and Y be two Polish spaces. Functions ƒ, g : X → Y are called equivalent if there exists a bijection φ from X onto itself such that g º φ = ƒ. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

Game-theoretic approach to the hereditary Baire property of Cp(Nf)

Michalewski H.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

135-140

We characterize second category P-filters on omega in terms of topological games. These characterizations use strong Choquet game gamma in the function space C[sub p](N[sub F]) associated with the filter F and a certain game delta played on the filter F. This complements earlier characterizations of hereditary Baire spaces C[sub p](N[sub F]), given by Gul'ko, Sokolov and Marciszewski.