New examples of hereditarily t-Baire spaces

• Autorzy: Kalenda O.
• Języki publikacji: EN

Abstrakty

EN

We introduce a new class of hereditarily t-Baire spaces (defined by G. Koumoullis (1993) - see below) which need not to have the restricted Baire property in a compactification - as an example serves the space (O,omega[sup 1])^A for A uncountable. We use this and a modification of a construction of D. Fremlin (1987) to get, under the assumption that there is a measurable cardinal, an example of a first class function of a hereditarily t-Baire space into a metric space which has no point of continuity, which shows, in answer to a question of G. Koumoullis (1993), that the cardinality restriction in his Theorem 4.1 cannot be dropped.

Słowa kluczowe

EN

countably compact space; first class function; hereditarily t-Baire space; restricted Baire property; weakly alpha-favorable space

PL

klasy funkcji; logika matematyczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 2
• Strony: 197--210
• Opis fizyczny: Bibliogr. 7 poz,

Twórcy

autor

Kalenda O.

• Department of Mathematical Analysis, Carles University, Sokolowska 83, 186 75 Praha 8, Czech Republik

Bibliografia

• [1] G. Koumoullis, A generalization of functions of the first class, Тороlоgy and its Applications, 50 (1993) 217-239.
• [2] P. Holicky, Remark on the point of continuity property and the strong Baire propеrtу in the restricted sense, Bull. Pol. Ас.: Math., 42 (1994) 85-95.
• [3] G. Koumoullis, Baire Categoтy in Spaces of Measures, Advanсеs in Math., 124 (1996) 1-24.
• [4] M. Wójcicka, Note on the Baire category in spaces of probability measuтes on nonsepaгable metrizable spaces, Bull. Pol. Ас.: Math., 33 (1985) 305-311.
• [5] H. E. White Jr, Topological spaces which are a-favorable for a player with perfect information, Proc. Amer. Math. Soc., 50 (1975) 477-482.
• [6] D. H. Fremlin, Measure-additive coverings and measurable selectors, Dissertationes Math., 260 (1987) 1-116.
• [7] O. Kalenda, Note on connections of the point of continuity property and Kuratowski рrоblem on function having the Baire property, Acta Univ. Carolinae, 38 (1) 1997) 3-12.