TOTAL ORDER MINIHEDRAL CONES
全序极小锥

A cone P in a Banach space E is called total order minihedral,if,under the partial or-dering introduced by P,every upper bounded total ordering set in E has a minimal upperbound.The main results of this paper are the following.Theorem 1.Regular cones are total order minihedral,but the converse is not true.Theorem 2.If Banach space E is weakly sequence complete,and P is a cone in E,thenthe following statements are equivalent:i)P is normal,ii)P is total order minihedral,iii)P is regular,iv)P is fully regular.Theorem 3.Suppose P is a total order minihedral cone,If,in addition,P is minihedr-al,then P is strongly minihedralTheorem 4.There exist total order minihedral cones which are not minihedral;thereexist minihedral cones which are not total order minihedral.