L-保序算子空間的ω-緊性

韓紅霞,孟廣武

(1.運(yùn)城學(xué)院應(yīng)用數(shù)學(xué)系,山西運(yùn)城 044000;2.聊城大學(xué)數(shù)學(xué)科學(xué)學(xué)院,山東聊城 252059)

L-保序算子空間的ω-緊性

韓紅霞1,孟廣武2

(1.運(yùn)城學(xué)院應(yīng)用數(shù)學(xué)系,山西運(yùn)城 044000;2.聊城大學(xué)數(shù)學(xué)科學(xué)學(xué)院,山東聊城 252059)

研究了L-保序算子空間的ω-緊性.借助于Hα-ω-開覆蓋,定義了L-保序算子空間的ω-緊性,證明了ω-緊集和ω-閉集之交是ω-緊的,ω-緊性被連續(xù)的廣義Zadeh型函數(shù)所保持,ω-緊性是L-好的推廣,Tychonoff乘積定理成立.此外,給出了ω-緊性的網(wǎng)式刻畫.

L-保序算子空間；Hα-ω-開覆蓋；ω-緊性

1 預(yù)備知識(shí)

在本文中,L表示F格,1與0分別表示其最大元與最小元.1X與0X分別表示LX的最大元與最小元.對(duì)a∈L,β(a)表示a的最大極小集,β?(a)=β(a)∩M(L).對(duì)A∈LX,β(A)表示A的最大極小集,β?(A)=β(A)∩M?(LX).記A(a)={x∈X|a∈β(A(x))}.其余未說明的概念和記號(hào)見文[1].

2 ω-緊性

3 Tychonoff乘積定理

4 ω-緊性的網(wǎng)式刻畫

[1]陳水利,董長(zhǎng)清.L-fuzzy保序算子空間[J].模糊系統(tǒng)與數(shù)學(xué),2002,16(專輯):36-41.

[2]黃朝霞.拓?fù)渖傻腇uzzy保序算子空間的ω-分解定理及ω-連通性理論[J].模糊系統(tǒng)與數(shù)學(xué),2004,18(專輯):180-183.

[3]Liu Yingming,Luo Maokang.Separations in lattice-valued induced spaces[J].Fuzzy Sets and System s,1990, 36:55-66.

[4]王戈平.完全分配格上的弱輔助序與廣義序同態(tài)[J].數(shù)學(xué)季刊,1988,3(4):76-83.

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

[6]ShiFugui,Zheng Chongyou.O-convergence of fuzzy netsand itsapp lications[J].Fuzzy Setsand System s,2003, 140:499-507.

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.

山東省自然科學(xué)基金(Y 2003A 01).

韓紅霞(1980-),碩士,講師,研究方向：模糊拓?fù)鋵W(xué).

2000M SC:54A 40