We study separate and joint properties of pointwise discontinuity, simple continuity and mildly continuity of functions of two variables. In particular it show that for a Baire space $X$, a Baire space $Y$ which has a countable pseudo-base and a metric space $Z$ a function $f:X\times Y\to Z$ is pointwise discontinuous if and only if $f$ satisfies $(\alpha, \beta)$-condition and condition (C) and $M=\{x\in X: \overline{C(f^x)}=Y\}$ is a residual subset of $X$. In addition, it was found of characterization of continuity for mappings of one and two variables
@article{282,
title = {Separate and joint properties of some analogues of pointwise discontinuity},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v58i0.282},
language = {EN},
url = {http://dml.mathdoc.fr/item/282}
}
Nesterenko, Vasyl'. Separate and joint properties of some analogues of pointwise discontinuity. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v58i0.282. http://gdmltest.u-ga.fr/item/282/