Classification of separately continuous mappings with values in o-metrizable spaces

Olena Karlova

Abstract

We prove that every vertically nearly separately continuous mapping defined on a product of a strong PP-space and a topological space and with values in a strongly o-metrizable space with a special stratification, is a pointwise limit of continuous mappings.

Keywords

Separately continuous mapping; Strong PP- space; Baire classification; Lebesgue classification

Full Text:

PDF

References

T. Banakh, (Metrically) quarter-stratifiable spaces and their applications, Math. Stud. 18, no. 1 (2002), 10–28.

M. Burke, Borel measurability of separately continuous functions, Topology Appl. 129, no. 1 (2003), 29–65. http://dx.doi.org/10.1016/S0166-8641(02)00136-0

R. Engelking, General Topology. Revised and completed edition. Heldermann Verlag, Berlin (1989).

H. Hahn, Reelle Funktionen.1.Teil. Punktfunktionen., Leipzig: Academische Verlagsge- sellscheft M.B.H. (1932).

A. Kalancha and V. Maslyuchenko, Cech-Lebesgue dimension and Baire classification of vector-valued separately continuous mappings, Ukr. Math. J. 55, no. 11 (2003), 1596–1599 (in Ukrainian).

O. Karlova, Baire classification of mappings which are continuous in the first variable and of the functional class in the second one, Math. Bull. NTSH. 2 (2005), 98–114 (in Ukrainian).

O. Karlova, Baire and Lebesgue classification of vector-values and multi-valued mappings, PhD thesis (2006) (in Ukrainian).

O. Karlova, Separately continuous o-discrete mappings, Bull. of Chernivtsi Nat. Univ., Mathematics 314–315 (2006), 77–79 (in Ukrainian).

O. Karlova and V. Maslyuchenko, Separately continuous mappings with values in non locally convex spaces, Ukr. Math. J. 59, no. 12 (2007), 1639–1646 (in Ukrainian). http://dx.doi.org/10.1007/s11253-008-0029-4

O. Karlova and V. Mykhaylyuk, Weak local homeomorphisms and B-favorable spaces, Ukr. Math. J. 60, no. 9 (2008), 1189–1195 (in Ukrainian). http://dx.doi.org/10.1007/s11253-009-0143-y

K. Kuratowski, Quelques probémes concernant les espaces métriques non-séparables, Fund. Math. 25 (1935), 534–545.

H. Lebesgue, Sur l’approximation des fonctions, Bull. Sci. Math. 22 (1898), 278–287.

V. Maslyuchenko, Separately continuous mappings and K¨othe spaces, Doctoral thesis (1999) (in Ukrainian).

D. Montgomery, Non-separable metric spaces, Fund. Math. 25 (1935), 527–533.

W. Moran, Separate continuity and supports of measures, J. London Math. Soc. 44 (1969), 320–324. http://dx.doi.org/10.1112/jlms/s1-44.1.320

V. Mykhaylyuk, Baire classification of separately continuous functions and Namioka property, Ukr. Math. Bull. 5, no. 2 (2008), 203–218 (in Ukrainian).

W. Rudin, Lebesgue first theorem, Math. Analysis and Applications, Part B. Edited by Nachbin. Adv. in Math. Supplem. Studies 78. Academic Press (1981), 741–747.

O. Sobchuk, PP-spaces and Baire classification, International Conference on Functional Analysis and its Applications, dedicated to the 110th anniversary of Stefan Banach. Book of abstracts, (2002), P. 189.

G. Vera, Baire mesurability of separately continuous functions, Quart. J. Math. Oxford 39, no. 2 (1988), 109–116. http://dx.doi.org/10.1093/qmath/39.1.109

Abstract Views

1100
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt