L-保序算子空间的ω-紧性

韩红霞,孟广武

(1.运城学院应用数学系,山西运城 044000;2.聊城大学数学科学学院,山东聊城 252059)

L-保序算子空间的ω-紧性

韩红霞1,孟广武2

(1.运城学院应用数学系,山西运城 044000;2.聊城大学数学科学学院,山东聊城 252059)

研究了L-保序算子空间的ω-紧性.借助于Hα-ω-开覆盖,定义了L-保序算子空间的ω-紧性,证明了ω-紧集和ω-闭集之交是ω-紧的,ω-紧性被连续的广义Zadeh型函数所保持,ω-紧性是L-好的推广,Tychonoff乘积定理成立.此外,给出了ω-紧性的网式刻画.

L-保序算子空间；Hα-ω-开覆盖；ω-紧性

1 预备知识

在本文中,L表示F格,1与0分别表示其最大元与最小元.1X与0X分别表示LX的最大元与最小元.对a∈L,β(a)表示a的最大极小集,β∗(a)=β(a)∩M(L).对A∈LX,β(A)表示A的最大极小集,β∗(A)=β(A)∩M∗(LX).记A(a)={x∈X|a∈β(A(x))}.其余未说明的概念和记号见文[1].

2 ω-紧性

3 Tychonoff乘积定理

4 ω-紧性的网式刻画

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[2]黄朝霞.拓扑生成的Fuzzy保序算子空间的ω-分解定理及ω-连通性理论[J].模糊系统与数学,2004,18(专辑):180-183.

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[4]王戈平.完全分配格上的弱辅助序与广义序同态[J].数学季刊,1988,3(4):76-83.

[5]He Wei.Generalized Zadeh function[J].Fuzzy Sets and System s,1998,97:381-386.

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ω-com pactness in L-order-preserving operator spaces

HAN Hong-xia1,MENG Guang-wu2

(1.Department of App lied Mathematics,Yuncheng College,Yuncheng,044000,China; 2.School of Mathem atics Science,Liaocheng University,Liaocheng,252059,China)

Theω-com pactness of L-order-preserving operator spaces is discussed.By m eans of Hα-ω-open cover,the notion ofω-com pactness of L-order-preserving operator spaces is introduced.It is p roved that the intersection of aω-com pact L-set and a closed L-set isω-com pact,thatω-com pactness is p reserved by continuously generalized Zadeh functions,thatω-com pactness is an L-good extension,and that the Tychonoff Theorem forω-com pactness is true.Moreover,ω-com pactness can also be characterized by nets.

L-order-preserving operator spaces,Hα-ω-open cover,ω-com pactness

O189

A

1008-5513(2009)02-0390-06

2007-07-10.

山东省自然科学基金(Y 2003A 01).

韩红霞(1980-),硕士,讲师,研究方向：模糊拓扑学.

2000M SC:54A 40