DIAGONAL OF GENERALIZED CL-FUNCTIONS ON EQUICONNECTED SPACES

M Husen Al Farisy; Atok Zulijanto

doi:10.22146/jmt.97744

DIAGONAL OF GENERALIZED CL-FUNCTIONS ON EQUICONNECTED SPACES

https://doi.org/10.22146/jmt.97744

M Husen Al Farisy^(1*), Atok Zulijanto⁽²⁾

(1) Universitas Gadjah Mada
(2) Universitas Gadjah Mada
(*) Corresponding Author

Abstract

In this paper we prove that the diagonal of a function of two variables which is continuous with respect to the first variable and generalized Lipschitz with respect to the second variable (in short generalized CL-functions) on equiconnected spaces is a stable Baire-1 class function.

Keywords

Stable Baire-1 functions; Generalized Lipschitz functions; Equiconnected spaces

Full Text:

PDF

References

Baire, R., Sur les fonctions de variables reelles, Annali di Matematica Pura ed Applicata, 3 (1899), 1-123.

Banakh, T. dan Kutsak, SM. dan Maslyuchenko, VK. dan Maslyuchenko, OV., Direct and Inverse Problems of Baire Classification of Integrals Depending on a Parameter, Ukrainian Mathematical Journal, 56 (2004), 1721-1737.

Banakh, T., (Metrically) quarter-stratifiable spaces and their applications in the theory of separately continuous functions, Matematychni Studii, 18 (2008), 10-28.

Banakh, T. dan Bokalo, B., On scatteredly continuous maps between topological spaces, Topology and its Applications, 157 (2010), 108-122.

Burke, M., Borel measurability of separately continuous functions, Topology and its Applications, 129 (2003), 29-65.

Császár, A. dan Laczkovich, M., Discrete and equal convergence, Studia Sci. Math. Hungar., 10 (1975), 463-472.

Karlova, O. dan Mykhaylyuk, V. dan Sobchuk, O., Diagonals of separately continuous functions and their analogs, Topology and its Applications, 160 (2013), 1-8.

Lebesgue, H., Sur les fonctions représentables analytiquement, Journal de Mathématiques Pures et Appliquées, 1 (1905), 139-216.

Miculescu, R., Some observations on generalized Lipschitz functions, The Rocky Mountain Journal of Mathematics, 37 (2007), 893-903.

Moran, W., Separate Continuity and Supports of Measures, Journal of the London Mathematical Society, s1-44 (1979), 320-324.

Munkres, J.R., Topology, Prentice Hall, Incorporated, London, 2000.

DOI: https://doi.org/10.22146/jmt.97744