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

Olena Karlova; Volodymyr Maslyuchenko; Volodymyr Mykhaylyuk

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1042-1053
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Olena Karlova, Volodymyr Maslyuchenko, and Volodymyr Mykhaylyuk. "Equiconnected spaces and Baire classification of separately continuous functions and their analogs." Open Mathematics 10.3 (2012): 1042-1053. <http://eudml.org/doc/269124>.

@article{OlenaKarlova2012,
abstract = {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.},
author = {Olena Karlova, Volodymyr Maslyuchenko, Volodymyr Mykhaylyuk},
journal = {Open Mathematics},
keywords = {Baire-one function; Function of the α-th Baire class; Separately continuous function; Equiconnected space; separately continuous function; equiconnected space; Baire classification of functions},
language = {eng},
number = {3},
pages = {1042-1053},
title = {Equiconnected spaces and Baire classification of separately continuous functions and their analogs},
url = {http://eudml.org/doc/269124},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Olena Karlova
AU - Volodymyr Maslyuchenko
AU - Volodymyr Mykhaylyuk
TI - Equiconnected spaces and Baire classification of separately continuous functions and their analogs
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1042
EP - 1053
AB - 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.
LA - eng
KW - Baire-one function; Function of the α-th Baire class; Separately continuous function; Equiconnected space; separately continuous function; equiconnected space; Baire classification of functions
UR - http://eudml.org/doc/269124
ER -

References

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  10. [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. [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. [12] Sobchuk O.V., Baire classification and Lebesgue spaces, Naukovij Visnik Cernivec’kogo Universitetu, Matematika, 2001, 111, 110–112 (in Ukranian) Zbl1065.54509
  13. [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. [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 Zbl0642.28002

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