On some property of functions defined on 𝐑² that are ℐ-approximately continuous with respect to one variable

Carrese, R.; Łazarow, E.

doi:10.1090/S0002-9939-1992-1097337-8

On some property of functions defined on $\mathbf {R}^2$ that are $\mathcal {I}$-approximately continuous with respect to one variable
HTML articles powered by AMS MathViewer

by R. Carrese and E. Łazarow PDF

Proc. Amer. Math. Soc. 116 (1992), 377-380 Request permission

Abstract:

Balcerzak, Lazarow, and Wilczyński proved that every separately $\mathcal {I}$-approximately continuous function is Baire 2. In this paper we shall prove that if $f$ is a function $\mathcal {I}$-approximately continuous with respect to one of its variables and of the $\alpha$-class of Baire with respect to the other one, then $f$ is of the $(\alpha + 1)$-class of Baire in ${R^2}$.

References

On one and two-dimensional

-densities and related kinds of continuity

13

Ewa Łazarow, On the Baire class of ${\scr I}$-approximate derivatives, Proc. Amer. Math. Soc. 100 (1987), no. 4, 669–674. MR 894436, DOI 10.1090/S0002-9939-1987-0894436-6
E. Łazarow, The coarsest topology for $I$-approximately continuous functions, Comment. Math. Univ. Carolin. 27 (1986), no. 4, 695–704. MR 874663
W. Poreda, E. Wagner-Bojakowska, and W. Wilczyński, A category analogue of the density topology, Fund. Math. 125 (1985), no. 2, 167–173. MR 813753, DOI 10.4064/fm-125-2-167-173
E. Wagner-Bojakowska and W. Poreda, The topology of $I$-approximately continuous functions, Rad. Mat. 2 (1986), no. 2, 263–277. MR 873702