VECTOR SUPERIOR AND INFERIOR

Source abstract

Let $(\cal Z \, , \, C)$ be an ordered Hausdorff real topological vector space. Some conditions for assuring that a nonempty set $K \subset {\cal Z}$ has a nonempty superior or inferior are established. Ordering-conically compact ordered Hausdorff real topological vector spaces are introduced so that in such a space every nonempty bounded below (respectively, bounded above) set has a nonempty inferior (respectively, superior).