湖南大学学报（自然科学版）
湖南大學學報（自然科學版）
호남대학학보（자연과학판）
JOURNAL OF HUNAN UNIVERSITY(NATURAL SCIENCES EDITION)
2014年
7期
113-116
,共4页
闭格%并不可约元%Locale%笛卡尔乘积%闭包运算
閉格%併不可約元%Locale%笛卡爾乘積%閉包運算
폐격%병불가약원%Locale%적잡이승적%폐포운산
closed lattice%join-irreducible element%Locale%Cartesian product%closure operation
对闭格进行研究，给出了闭格的等价刻画，讨论了闭格与 Locale 的关系，并证明了闭格的笛卡尔乘积仍是闭格。同时，得到了闭格在保任意并的满态射下仍是闭格，最后证明了闭格在闭包运算下的像是闭格。
對閉格進行研究，給齣瞭閉格的等價刻畫，討論瞭閉格與 Locale 的關繫，併證明瞭閉格的笛卡爾乘積仍是閉格。同時，得到瞭閉格在保任意併的滿態射下仍是閉格，最後證明瞭閉格在閉包運算下的像是閉格。
대폐격진행연구，급출료폐격적등개각화，토론료폐격여 Locale 적관계，병증명료폐격적적잡이승적잉시폐격。동시，득도료폐격재보임의병적만태사하잉시폐격，최후증명료폐격재폐포운산하적상시폐격。
In this paper,we investigated some properties of the closed lattices and gave their character-izations.The relationship between the Locale and the closed lattice was investigated.It is proved that the Cartesian product of the close lattice is still closed lattice.Moreover,we obtained the result that the closed lattice under a surj ective map preserving arbitrary sups is still the closed lattice.Finally,we studied the property of the image of the closed lattice under the closure operator.
