  A double sequence $\textbf{x}=\{x_{k,l}\}$ of points in $\textbf{R}$ is
slowly oscillating if for any given $\varepsilon>0$, there exist
$\alpha=\alpha(\varepsilon)>0$, $\delta=\delta (\varepsilon) >0$, and
$N=N(\varepsilon)$ such that $|x_{k,l}-x_{s,t}|<\varepsilon$ whenever $k,l\geq
N(\varepsilon)$ and $k\leq s \leq (1+\alpha)k$, $l\leq t \leq (1+\delta)l$. We
study continuity type properties of factorable double functions defined on a
double subset $A\times A$ of $\textbf{R}^{2}$ into $\textbf{R}$, and obtain
interesting results related to uniform continuity, sequential continuity, and a
newly introduced type of continuity of factorable double functions defined on a
double subset $A\times A$ of $\textbf{R}^{2}$ into $\textbf{R}$.
