Simple Order Product/Examples

Examples of Simple Order Products

Unit Square with Open Side

Consider the simple order product of the real intervals $\hointr 0 1$ and $\closedint 0 1$ under the usual ordering:

$\struct {T, \preccurlyeq_s} := \struct {\hointr 0 1, \le} \otimes^s \struct {\closedint 0 1, \le}$

$\struct {T, \preccurlyeq_s}$ has one minimal element:

$\tuple {0, 0}$

which is also the smallest element: of $\struct {T, \preccurlyeq_s}$.

$\struct {T, \preccurlyeq_s}$ has no greatest element and no maximal elements.