A double sequence $\{ x_{ k,l}\}$ is quasi-Cauchy if given an $\epsilon > 0$ there exists an $N \in { \bf N}$ such that $$\max_{ r,s= 1\mbox{ and/or} 0} \left \{ |x_{ k,l} - x_{ k+r,l+s}|< \epsilon\right \} .$$ We study continuity type properties of factorable double functions defined on a double subset $A\times A$ of ${ \bf R}^{ 2}$ into $\textbf{ R}$, and obtain interesting results related to uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset $A\times A$ of ${ \bf R}^{ 2}$ into $\textbf{ R}$.
Categories: math.GM