STRONG CONTINUITY OF FUNCTIONS FROM TWO VARIABLES

The concept of continuity in a strong sense for the case functions with values metric spaces is studied. separate and joint properties this are investigated, several results by Russell generalized. A function $f:X \times Y \to Z$ strongly continuous respect to $x$ /$y$/ at point ${(x_0, y_0)\in X Y}$ provided an arbitrary $\varepsilon> 0$ there neighborhoods $U$ $x_0$ $X$ $V$ $y_0$ $Y$ such that $d(f(x, y), f(x_0, y)) <\varepsilon$ /$d((x, f (x, y_0))<\varepsilon$/ all $x \in U$ $y V$. $f$ said be if it so every $(x, y)\in Y$. Note that, real two variables, notion given variable same equivalent. In 1998 Dzagnidze established variables over set only each variables. Here we transfer result space: topological spaces, $Z$ space $y$ $(x_0, y_0) Y$, then jointly $f_{y}$ $y\in It obvious $y$, but not vice versa. On other hand, or implies respectively. Thus, separately continuous. Also, $y$.