幂格与商格的关系

该文在文［1］中幂格概念的基础上,得到了幂格的一个充要条件,给出了正则幂格、相对幂格的概念,并讨论了商格与正则幂格、相对幂格的关系.〖HT5”H〗关键词:〖HT5”SS〗格;幂格;商格;正则幂格;相对幂格.     

分配格上的全序幂格

研究了分配格上的幂格的偏序关系,给出了分配格上的幂格是链格的充要条件.     

Lattice of subgroups

Let D be a subgroup of the group G. The lattice of intermediate subgroups is studied. The subgroup F (D F G) is said to be D-complete, if D^F=u:u F>=F. Let F be the subset of all D-complete intermediate subgroups. The system {F, N_G(F)} is a fan for D in G (RZhMat, 1980, 5A208) if and only if D^x> is a D-complete subgroup for any x G. The set {F_ga} coincides with the collection of subgroups of the form D^A (1 A C G) if and only if for any x G the subgroup D, D^x is D-complete. The last condition holds, for example, for a pronormal subgroup D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 13–19, 1980.     

Lattice Realcompactifications

Summary The theory of realcompactness is generalized to a lattice setting and studied from five different viewpoints. The relationships between these viewpoints is given and applications indicated. Entrata in Redazione il 10 aprile 1974.     

幂格与幂集格的关系

由幂格的定义知 ,幂格与幂集格是不同的 ,然而它们却有一定的联系 .本文在幂格概念的基础上 ,进一步地讨论幂格和幂集格在一定条件下的联系 .     

Lattice points

Journal of Fourier Analysis and Applications -     

Z-半连续格

作为连续格和半连续格的公共推广,引入了广义理想子系统Z、Z-半连续格及强Z-连续格的概念,讨论了它们的基本性质和Z-半连续格的函数空间的结构,给出了强Z-连续格到方体的嵌入,证明了当子系统Z满足一定条件时,Z-半连续格范畴SCLZ是笛卡儿闭的。     

格的凸子格格与幂格

研究格的凸子格的性质,建立格的非空凸子格组成的幂格与幂格的联系,证明在同构意义下,分配格的幂格都是它的非空凸子格组成的幂格的子格。     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

Lattice properties of epigroups

The aim of this paper is to give a survey of the first advances in the study of diverse interconnections between epigroups and their subepigroup lattices.     

Lattice of generalized topologies

We prove that the family of all generalized topologies on a nonempty set is a lattice, neither distributive nor complemented. We define the direct sum of two generalized topologies and characterize the direct sum.     

Lattice closures of polyhedra

Mathematical Programming - Given $$P\subset {\mathbb {R}}^n$$, a mixed-integer set $$P^I=P\cap ({\mathbb {Z}}^{t}\times {\mathbb {R}}^{n-t}$$), and a k-tuple of n-dimensional integral vectors...     

模糊概念格

概念格是研究和处理概念内涵与外延确定性关系的数学方法 ,已成为一种有效的数据分析方法。本文进一步探讨概念内涵与外延的不确定关系的模糊映射 ,给出相应的隶属函数的一些基本数学性质 ,证明全体模糊概念构成一个完全格。     

Lattice complete graphs

We study the properties of graphs that can be placed in a rectangular lattice so that all vertices located in the same (horizontal or vertical) row be adjacent. Some criterion is formulated for an arbitrary graph to be in the specified class.     

Excess of a Lattice

 A pair (x,y) of elements in a lattice is mismatching if x is join-irreducible, y is meet-irreducible, and xy. The excess of a lattice L is defined by ex(L):=|L|− min{|V _x |+|I _y |:(x,y) is mismatching}, where V _x (I _y ) is the principal filter (ideal) generated by x(y), respectively. In the first half of this paper, it is shown that a lattice has excess zero (one) if and only if it is isomorphic to a Boolean lattice (one of a chain of length two, a diamond, and a pentagon), respectively. In the second half, we show that for each relatively complemented lattice which is not Boolean, its size is at most five times its excess. Moreover we determine extremal configurations. Received: September 2, 1999 Final version received: July 25, 2000 Acknowledgments. The author thanks the referee for constructive comments. Present address: Bureau of Human Resources, National Personnel Authority, 1-2-3 Kasumigaseki, Chiyoda-ku, Tokyo 100-8913, Japan. e-mail: abetet@jinji.go.jp