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2012 | 10 | 3 | 1042-1053
Tytuł artykułu

Equiconnected spaces and Baire classification of separately continuous functions and their analogs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
3
Strony
1042-1053
Opis fizyczny
Daty
wydano
2012-06-01
online
2012-03-24
Twórcy
Bibliografia
  • [1] Banakh T.O., (Metrically) quarter-stratifiable spaces and their applications, Mat. Stud., 2002, 18(1), 10–28
  • [2] Burke M.R., Borel measurability of separately continuous functions, Topology Appl., 2003, 129(1), 29–65 http://dx.doi.org/10.1016/S0166-8641(02)00136-0
  • [3] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
  • [4] Engelking R., Theory of Dimensions, Finite and Infinite, Sigma Ser. Pure Math., 10, Heldermann, Lemgo, 1995
  • [5] Hahn H., Reelle Funktionen. I: Punktfunktionen, Mathematik und ihre Anwendungen in Monographien und Lehrbüchern, 13, Leipzig, Academische Verlagsgesellscheft, 1932
  • [6] Kalancha A.K., Maslyuchenko V.K., The Lebesgue-Čech dimension and Baire classification of vector-valued separately continuous mappings, Ukraïn. Mat. Zh., 2003, 55(11), 1576–1579 (in Ukrainian)
  • [7] Karlova O., Baire classification of mappings which are continuous in the first variable and of the functional class α in the second one, Matematychny Visnyk NTSH, 2005, 2, 98–114 (in Ukrainian)
  • [8] Lebesgue H., Sur l’approximation des fonctions, Bull. Sci. Math., 1898, 22, 278–287
  • [9] Moran W., Separate continuity and supports of measures, J. London Math. Soc., 1969, 44, 320–324 http://dx.doi.org/10.1112/jlms/s1-44.1.320
  • [10] Mykhaylyuk V.V., Baire classification of separately continuous functions and the Namioka property, Ukr. Mat. Visn., 2008, 5(2), 203–218 (in Ukrainian)
  • [11] Rudin W., Lebesgue’s first theorem, In: Mathematical Analysis and Applications, Part B, Adv. in Math. Suppl. Stud., 7b, Academic Press, New York-London, 1981, 741–747
  • [12] Sobchuk O.V., Baire classification and Lebesgue spaces, Naukovij Visnik Cernivec’kogo Universitetu, Matematika, 2001, 111, 110–112 (in Ukranian)
  • [13] Sobchuk O.V., PP-spaces and Baire classification, In: Book of abstracts of the International Conference on Functional Analysis and its Applications dedicated to the 110th anniversary of Stefan Banach, Lvov, May 28–31, 2002, Ivano Franko National University, Lvov, 2002, 189
  • [14] Vera G., Baire measurability of separately continuous functions, Quart. J. Math. Oxford, 1988, 39(153), 109–116 http://dx.doi.org/10.1093/qmath/39.1.109
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0016-8
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