Let $R$={$((x_1,y_1),(x_2,y_2))$:$x_1\le x_2, y_1\le y_2$} find the maximal chaings.
Could it be that every maximal chains is of the form {$(a,b)+t(1,1)|t\in\Bbb{R}$} such that every other chain of the form {$n(a,b)+m(1,1)|m\in\Bbb{R}$}is the same one? I would appreciate your help...