%0 Journal Article
%T TOTAL ORDER MINIHEDRAL CONES<br>全序极小锥
%A DU YI-HONG
%A <br>杜一宏
%J 系统科学与数学
%D 1988
%I 
%X 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.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=77638422D605D7F6DC15704CD379C885&yid=0702FE8EC3581E51&vid=5D311CA918CA9A03&iid=CA4FD0336C81A37A&sid=FE1A8AC7B3463DB5&eid=10886C0681CB8991&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=6&reference_num=0