本文主要研究内容
作者韩雪梅（2019）在《两类广义正则半群的若干研究》一文中研究指出：本文主要研究两类广义正则半群,给出了它们的某些性质定理和结构定理.其主要思想是利用广义格林关系来研究广义正则半群的性质及结构.本文共分三章,具体内容如下:第一章:本章研究了强U-HU-富足半群上的同余及性质,分别给出了包含在LU RU,HU中的最大同余,利用这三个同余得到若干等价关系,最后利用幂等元半格U,刻画了强U-HU-富足半群的性质.主要结论如下:定理1.2.2若S为强U-LU-富足半群,则μ(?)U={(a,b)∈S×S|(?)u∈U1,(ua,ub)∈LU}={(a,b)∈S×S|(?)u∈U1,(ua)*=(ub)*}.是包含在LU中的最大同余,定理1.2.3 若S为强U-RU-富足半群.则μ(?)U={(a,b)∈S×S|(?)∈U1,(au.bu)∈RU}={(a,b)∈S×S|(?)u∈U1,(au)+=(bu)+}.是包含在RU中的最大同余.定理1.2.4 若S为强U-HU-富足半群,则μ={(a,b)∈S×S|(?)∈U1,(ua.ub)∈(?)(au,bu)∈LU}={(a,b)∈S×S|(?)u∈U1,(ua)*=(ub*).(au)+=(bu)+}.是包含在HU中的最大同余.定理1.2.8 若S为强U-LU-富足半群.则下列条件等价:(1)S=U={uμ(?)U|u∈U};(2)μ(?)u=(?);(3)对(?)u∈U,a∈S,(au,ua)∈(?).定理1.2.9 若S为强UU-RU-富足半群,则下列条件等价:(1)S=U={Uμ(?)u|uκU];(2)μ(?)U=(?);(3)对(?)u∈U,a∈S,(au,ua)∈RU.定理1.2.10 若S为强U-HU-富足半群,则有(1)For(?)a,b∈S,a*=a+,b*=b+;(2)LU=RU=HU;(3)S的每个HU-类只含一个U中幂等元;(4)是是S的中心.定理1.2.12 设S为强U-LU-富足半群,若S是强U-LU-富足半群,则对(?)a ∈ S,有a*=a*.定理1.2.13 设S为强U-RU-富足半群,若S是强U-RU-富足半群,则对(?)a ∈ S,有a+=a+.定理1.2.14 设S为强U-HU-富足半群,若S/μ是强U/μ-HU/μ-富足半群,则对(?)a ∈S,有(aμ)*=a*μ,(aμ)+=a+μ.定理1.2.15 设S为强U-LU-富足半群,若S是强U-LU-富足半群,则S是右基本的.定理1.2.16 设S为强U-RU-富足半群,若S是强U-RU-富足半群,则S是左基本的.定理1.2.17设S为强U-HU-富足半群,若S/μ是强U/μ-HU/μ-富足半群,则S/μ是基本的.第二章:本章主要刻画了型A-RU-富足半群的平移壳的结构.首先定义了型A-RU-富足半群,而后证明了型A-RU-富足半群的平移壳仍为型A-RU-富足半群.主要结论如下：定理2.2.9 型A-RU-富足半群的平移壳仍为型A-RU-富足半群.推论2.2.10 型A-RU-富足半群的平移壳仍为型A-RU-富足半群.第三章:本章定义了LR-C-good B-quasi-Ehresmann 半群,并给出了LR-C-good B-quasi-Ehresmann半群的结构.主要结论如下:定理3.2.1 设S为半群,则存在B(?)E(S)使得S(B)是一个LR-C-goodB-quasi-Ehresmann半群(?)S是有公共C-goodB-quasi-Ehresmann半群分量T=[Y;Tα]的左C-goodB-quasi-Ehresmann半群S1=[Y;Iα×Tα]和右C-good/B-quasi-Ehresmnann半群S2=[Y;Tα× Λα]关于半群同态φ:(i,x)→x,(i,x)∈S1和ψ:(x,λ)→x,(x,λ)∈S2的一个织积S1×Tφ,ψS2,且使得B(S)(?)(C(B(S1))× B(S2))∪(B(S1× C(B(S2))).其中B(S)=∪α∈Y((Iα×{1Tα)×({1Tα}×Λα)),B(S1)-∪α∈Y((Iα×{1Tα}),B(S2)=∪α∈Y({1Tα}×Λα)且C(B(Si))是B(Si)的中心,i=1,2.定理 3.2.2 设T=|Y;Tα]是一个C-good B-quasi-Ehresmann半群.I=[Y;Iα]是一个左正则带且Λ=[Y;Λα]是一个右正则带.若映射ξ:∪α∈Y(Iα×Tα)→τl(I),(i,x)→(i,x)#η:∪α∈Y(Tα×Λα)→τr(Λ),(x,λ)→(x,λ)*满足下列条件:(L1)若(i,x)∈Iα × Tα且j∈Iβ,则(i,x)#j∈Iαβ;(R1)若(x,λ)∈Tα×Λα且μ∈Λβ,则μ(x,λ)*∈Λαβ;(L2)若(L1)中,若α≤β则(i,x)#j=i;(R2)若(R1)中,若α ≤β,则μ(x,λ)*=λ;(L3)若(i,x)∈Iα×Tα且(j,y)∈Iβ×Tβ，则(i,x)#(j,y)#=((i,x)#j,xy)#;(R3)若(x,λ)∈Tα×Λα且(y,μ)∈Tβ×Λβ,则(x,λ)*(y,μ)*=(xy,λ(y,μ)*)*;(P)若i∈Iα,λ∈Λα,则(?)β≤α,(?)j∈Iβ,(i,1Tα)#j=j(这时根据(L2)有|Iα|==1)或(?)β≤α,(?)μ∈Λβ,μ(1Tα,λ)*=μ(这时根据(R2)有|Λα|=1).则S(B)=∪α∈Y(Iα×Tα×Λα)关于二元运算(i,x,λ)(j,y,μ)=((i,x)#j,xy,λ(y,μ)*)构成一个LR-C-goodB-quasi-Ehresmann半群,其中B=∪α∈Y(Iα × {1Tα} ×Λα).反之,每个LR-C-goodB-quasi-Ehresmann半群都可如此构造.定理 3.2.3 设T=[Y;Tα]是一个C-goodB-quasi-Ehresmann半群,对于(?)α ∈Y,Iα和Λα是两个非空集合且Iα∩ Iβ=(?)=Λα∩ Λβ(α≠β).作直积Pα=Iα×Tα和Qα=Tα×Λα(α ∈Y).记S=∪α∈Y(Iα×Tα×Λα)且B=∪α∈Y(Iα× {1Tα} × Λα).对(?)α,γ ∈Y,γ ≤ α时,设映射ψα,γ:Pα→τl(Iγ),(i,x)→ψα,γ(i,x)φα,γ:Qα→τr(Λγ),(x,λ)→φα,γ(x,λ)满足下列条件:(L1)若(i,x)∈Pα且j ∈Iα,则ψα,α(i,x)j=i;(R1)若(x,λ)∈Qα且μ∈Λα,则μφα,α(x,λ)=λ;(L2)若(i,x)∈ Pα且(j,y)∈Pβ,则ψα,αβ(i,x)ψβ,αβ(j,y)=<ψα,αβ(i,x)ψβ,αβ(j,y)>;(R2)若(x,λ)∈ Qα且(y,μ)∈Qβ,则φα,αβ(x,λ)φβ,αβ(y,μ)=<φα,αβ(x,λ)φβ,αβ(y,μ)>;(L3)若在(L2)中,δ≤αβ,则ψαβ,δ(k,xy)=ψα,δ(i,x)ψβδ(j,y),其中k=<ψα,αβ(i,x)ψβ,αβ(j,y)>;(R3)若在(R2)中,δ≤αβ，则φαβ,δ(xy,v)=φα,δ(x,λ)φβ,δ(y,μ),其中v=<φα,αβ(x,λ)φβ,αβ(y,μ)>;(P)若i ∈Iα,λ∈Λα,则(?)γ≤α,ψα,γ(i,1Tα)=εIγ,(εIγ是Iγ的恒等映射)(这时根据(L1)有|Iα|=1)或(?)γ≤α,φα,γ(1Tα,λ)=εΛγ,(εΛγ是Λα上的单位映射)(这时根据(R1)有|Λα|=1).则S(B)=∪α∈Y(Iα×Tα×Λα)关于二元运算(i,x,λ)(j,y,μ)-(<ψα,αβ(i,x)ψβ,αβ(j,y)>,xy,<φα,αβ(x,λ)φβ,αβ(y,μ)>).构成一个LR-C-goodB-quasi-Ehresmann半群,其中B=∪α∈Y(Iα×{1Tα} ×Λα).反之,每个LR-C-goodB-quasi-Ehresmann半群都可如此构造.推论 3.2.4 设T=[Y;Tα]是一个C-Ehresrmann半群,I=[Y;Iα]是一个左正则带且Λ=[Y;Λα]是一个右正则带.若映射ξ:∪α∈Y(Iα × Tα)→τl(I),(i,x)→(i,x)#η:∪α∈Y(Tα × Λα)→τr(Λ),(x,λ)→(x,λ)*满足下列条件:(L1)若(i,x)∈ Iα×Tα且j∈I3，则(i,x)#j∈Iαβ:(R1)若(x,λ)∈Tα× Λα.且μ ∈ Λβ,则μ(x,λ)*Λαβ;(L2)在(L1)中,若α≤β,则(i,x)#j=i;(R2)在(R1)中,若α ≤β,则μ(x,λ)*=λ:(L3)若(i.x)Iα × Tα且(j,y)∈Iβ× Tβ则(i,x)#(j,y#=((i,x)#j,xy)#;(R3)若(x,λ)∈Tα×Λα且(y,μ)∈Tβ×Λβ.则(x,λ)*(y,μ)*=(xy,λ(y,μ)*)*;(P)若i∈Iα,λ ∈Λα,则(?)β≤α,(?)j∈I3,(i,1Tα)#j=j(这时根据(L2)有|Iα|=1)或(?)β≤ α,∈ μ(1Tα,λ)*=μ(这时根据(R2)有|Aα|=1).则S(B)二∪α∈Y(Iα × Tα × Aα)关于二元运算(i,x,λ)(j,y,μ)=((i,x)#j,xy,λ(y,μ)*)构成一个LR-C-Ehresmann,,其中B=Uα∈Y(Iα × {1Tα} × Aα).反之,每个LR-C-Ehresmannn半群都可如此构造.推论3.2.5 设T=[Y;Tα]是一个C-Ehmann半群,对于(?)α∈Y,Iα和Λα是两个非空集合且Iα ∩Iβ=(?)=Λα ∩ Λ3(α≠β).作直积Pα=Iα × Tα.和Qα=Tα×Λα(α∈S).记S=∪α∈Y(Iα ×Tα×Λα)且B=∪α∈Y(Iα×{1Tα}×Λα).对(?)α,γ∈Y，γ≤ α时,设映射ψα,γ：Pα→τl(Iγ),(i,x)→ψα,γ(i,x)φα,γ→τr(Λγ),(x,λ)→φα,γ(x,λ)满足下列条件:(L1)若(i,x)∈Pα且j∈Iα,则ψα,α(i,x)j=i;(R1)若(x,λ)∈ Qα且μ∈Λα,则μφα,α(x,λ)=λ;(L2)若(i,x)∈&且(j,y)∈Pβ 则ψα,αβ(i,x)ψβ,αβ(j,y)=ψα,αβ(i,x)ψβαβ(j,y)〉;(R2)若(x,λ)∈ Qα且(y,μ)∈Qβ,则φα,αβ(x,λ)φβ,αβ(y,μ)=φα,αβ(x,λ)φβ,αβ(y,μ)〉(L3)若在(L2)中,δ≤αβ,则ψα,βδ(k,xy)=ψα,δ(i,x)ψβ,δ(j,y),其中k=〈ψα,αβ(i,x)ψβ,αβ(j,y)〉;(R3)若在(R2)中,δ ≤αβ,则φαβ,δ(xy,v)=φα,δ(x,λ)φβ,δ(y,μ),其中v=〈φα,αβ(x,λ)φβ,αβ(y,μ)〉;(P)若i∈Iα,λ ∈Λα,则(?)γ≤α,ψα,γ(i,1Tα)=εIγ,(εIγ是Iγ上的恒等映射)(这时根据(La)有|Iα|=1)或(?)γ≤α,=∈Λγ,(∈Λγ是Λγ上的单位映射)(这时根据(R1)有|Λα|=1).则S(B)=UαY,(Jα × Tα × Λα)关于二元运算(i,x,λ)(j,y,μ(〈ψα,αβ(i,x)ψβ,αβ(j,y),xy,〈φα,αβ(x,λ)〉,xy〈φα,αβ(x,λ)φβ,αβ(y,μ)〉)构成一个LR-C-Ehresmann半群,其中B=∪α∈Y(Iα×{1Tα}×Λα).反之,每个LR-C-Ehresmann半群都可如此构造.
Abstract
ben wen zhu yao yan jiu liang lei an yi zheng ze ban qun ,gei chu le ta men de mou xie xing zhi ding li he jie gou ding li .ji zhu yao sai xiang shi li yong an yi ge lin guan ji lai yan jiu an yi zheng ze ban qun de xing zhi ji jie gou .ben wen gong fen san zhang ,ju ti nei rong ru xia :di yi zhang :ben zhang yan jiu le jiang U-HU-fu zu ban qun shang de tong yu ji xing zhi ,fen bie gei chu le bao han zai LU RU,HUzhong de zui da tong yu ,li yong zhe san ge tong yu de dao re gan deng jia guan ji ,zui hou li yong mi deng yuan ban ge U,ke hua le jiang U-HU-fu zu ban qun de xing zhi .zhu yao jie lun ru xia :ding li 1.2.2re Swei jiang U-LU-fu zu ban qun ,ze μ(?)U={(a,b)∈S×S|(?)u∈U1,(ua,ub)∈LU}={(a,b)∈S×S|(?)u∈U1,(ua)*=(ub)*}.shi bao han zai LUzhong de zui da tong yu ,ding li 1.2.3 re Swei jiang U-RU-fu zu ban qun .ze μ(?)U={(a,b)∈S×S|(?)∈U1,(au.bu)∈RU}={(a,b)∈S×S|(?)u∈U1,(au)+=(bu)+}.shi bao han zai RUzhong de zui da tong yu .ding li 1.2.4 re Swei jiang U-HU-fu zu ban qun ,ze μ={(a,b)∈S×S|(?)∈U1,(ua.ub)∈(?)(au,bu)∈LU}={(a,b)∈S×S|(?)u∈U1,(ua)*=(ub*).(au)+=(bu)+}.shi bao han zai HUzhong de zui da tong yu .ding li 1.2.8 re Swei jiang U-LU-fu zu ban qun .ze xia lie tiao jian deng jia :(1)S=U={uμ(?)U|u∈U};(2)μ(?)u=(?);(3)dui (?)u∈U,a∈S,(au,ua)∈(?).ding li 1.2.9 re Swei jiang UU-RU-fu zu ban qun ,ze xia lie tiao jian deng jia :(1)S=U={Uμ(?)u|uκU];(2)μ(?)U=(?);(3)dui (?)u∈U,a∈S,(au,ua)∈RU.ding li 1.2.10 re Swei jiang U-HU-fu zu ban qun ,ze you (1)For(?)a,b∈S,a*=a+,b*=b+;(2)LU=RU=HU;(3)Sde mei ge HU-lei zhi han yi ge Uzhong mi deng yuan ;(4)shi shi Sde zhong xin .ding li 1.2.12 she Swei jiang U-LU-fu zu ban qun ,re Sshi jiang U-LU-fu zu ban qun ,ze dui (?)a ∈ S,you a*=a*.ding li 1.2.13 she Swei jiang U-RU-fu zu ban qun ,re Sshi jiang U-RU-fu zu ban qun ,ze dui (?)a ∈ S,you a+=a+.ding li 1.2.14 she Swei jiang U-HU-fu zu ban qun ,re S/μshi jiang U/μ-HU/μ-fu zu ban qun ,ze dui (?)a ∈S,you (aμ)*=a*μ,(aμ)+=a+μ.ding li 1.2.15 she Swei jiang U-LU-fu zu ban qun ,re Sshi jiang U-LU-fu zu ban qun ,ze Sshi you ji ben de .ding li 1.2.16 she Swei jiang U-RU-fu zu ban qun ,re Sshi jiang U-RU-fu zu ban qun ,ze Sshi zuo ji ben de .ding li 1.2.17she Swei jiang U-HU-fu zu ban qun ,re S/μshi jiang U/μ-HU/μ-fu zu ban qun ,ze S/μshi ji ben de .di er zhang :ben zhang zhu yao ke hua le xing A-RU-fu zu ban qun de ping yi ke de jie gou .shou xian ding yi le xing A-RU-fu zu ban qun ,er hou zheng ming le xing A-RU-fu zu ban qun de ping yi ke reng wei xing A-RU-fu zu ban qun .zhu yao jie lun ru xia ：ding li 2.2.9 xing A-RU-fu zu ban qun de ping yi ke reng wei xing A-RU-fu zu ban qun .tui lun 2.2.10 xing A-RU-fu zu ban qun de ping yi ke reng wei xing A-RU-fu zu ban qun .di san zhang :ben zhang ding yi le LR-C-good B-quasi-Ehresmann ban qun ,bing gei chu le LR-C-good B-quasi-Ehresmannban qun de jie gou .zhu yao jie lun ru xia :ding li 3.2.1 she Swei ban qun ,ze cun zai B(?)E(S)shi de S(B)shi yi ge LR-C-goodB-quasi-Ehresmannban qun (?)Sshi you gong gong C-goodB-quasi-Ehresmannban qun fen liang T=[Y;Tα]de zuo C-goodB-quasi-Ehresmannban qun S1=[Y;Iα×Tα]he you C-good/B-quasi-Ehresmnannban qun S2=[Y;Tα× Λα]guan yu ban qun tong tai φ:(i,x)→x,(i,x)∈S1he ψ:(x,λ)→x,(x,λ)∈S2de yi ge zhi ji S1×Tφ,ψS2,ju shi de B(S)(?)(C(B(S1))× B(S2))∪(B(S1× C(B(S2))).ji zhong B(S)=∪α∈Y((Iα×{1Tα)×({1Tα}×Λα)),B(S1)-∪α∈Y((Iα×{1Tα}),B(S2)=∪α∈Y({1Tα}×Λα)ju C(B(Si))shi B(Si)de zhong xin ,i=1,2.ding li 3.2.2 she T=|Y;Tα]shi yi ge C-good B-quasi-Ehresmannban qun .I=[Y;Iα]shi yi ge zuo zheng ze dai ju Λ=[Y;Λα]shi yi ge you zheng ze dai .re ying she ξ:∪α∈Y(Iα×Tα)→τl(I),(i,x)→(i,x)#η:∪α∈Y(Tα×Λα)→τr(Λ),(x,λ)→(x,λ)*man zu xia lie tiao jian :(L1)re (i,x)∈Iα × Tαju j∈Iβ,ze (i,x)#j∈Iαβ;(R1)re (x,λ)∈Tα×Λαju μ∈Λβ,ze μ(x,λ)*∈Λαβ;(L2)re (L1)zhong ,re α≤βze (i,x)#j=i;(R2)re (R1)zhong ,re α ≤β,ze μ(x,λ)*=λ;(L3)re (i,x)∈Iα×Tαju (j,y)∈Iβ×Tβ，ze (i,x)#(j,y)#=((i,x)#j,xy)#;(R3)re (x,λ)∈Tα×Λαju (y,μ)∈Tβ×Λβ,ze (x,λ)*(y,μ)*=(xy,λ(y,μ)*)*;(P)re i∈Iα,λ∈Λα,ze (?)β≤α,(?)j∈Iβ,(i,1Tα)#j=j(zhe shi gen ju (L2)you |Iα|==1)huo (?)β≤α,(?)μ∈Λβ,μ(1Tα,λ)*=μ(zhe shi gen ju (R2)you |Λα|=1).ze S(B)=∪α∈Y(Iα×Tα×Λα)guan yu er yuan yun suan (i,x,λ)(j,y,μ)=((i,x)#j,xy,λ(y,μ)*)gou cheng yi ge LR-C-goodB-quasi-Ehresmannban qun ,ji zhong B=∪α∈Y(Iα × {1Tα} ×Λα).fan zhi ,mei ge LR-C-goodB-quasi-Ehresmannban qun dou ke ru ci gou zao .ding li 3.2.3 she T=[Y;Tα]shi yi ge C-goodB-quasi-Ehresmannban qun ,dui yu (?)α ∈Y,Iαhe Λαshi liang ge fei kong ji ge ju Iα∩ Iβ=(?)=Λα∩ Λβ(α≠β).zuo zhi ji Pα=Iα×Tαhe Qα=Tα×Λα(α ∈Y).ji S=∪α∈Y(Iα×Tα×Λα)ju B=∪α∈Y(Iα× {1Tα} × Λα).dui (?)α,γ ∈Y,γ ≤ αshi ,she ying she ψα,γ:Pα→τl(Iγ),(i,x)→ψα,γ(i,x)φα,γ:Qα→τr(Λγ),(x,λ)→φα,γ(x,λ)man zu xia lie tiao jian :(L1)re (i,x)∈Pαju j ∈Iα,ze ψα,α(i,x)j=i;(R1)re (x,λ)∈Qαju μ∈Λα,ze μφα,α(x,λ)=λ;(L2)re (i,x)∈ Pαju (j,y)∈Pβ,ze ψα,αβ(i,x)ψβ,αβ(j,y)=<ψα,αβ(i,x)ψβ,αβ(j,y)>;(R2)re (x,λ)∈ Qαju (y,μ)∈Qβ,ze φα,αβ(x,λ)φβ,αβ(y,μ)=<φα,αβ(x,λ)φβ,αβ(y,μ)>;(L3)re zai (L2)zhong ,δ≤αβ,ze ψαβ,δ(k,xy)=ψα,δ(i,x)ψβδ(j,y),ji zhong k=<ψα,αβ(i,x)ψβ,αβ(j,y)>;(R3)re zai (R2)zhong ,δ≤αβ，ze φαβ,δ(xy,v)=φα,δ(x,λ)φβ,δ(y,μ),ji zhong v=<φα,αβ(x,λ)φβ,αβ(y,μ)>;(P)re i ∈Iα,λ∈Λα,ze (?)γ≤α,ψα,γ(i,1Tα)=εIγ,(εIγshi Iγde heng deng ying she )(zhe shi gen ju (L1)you |Iα|=1)huo (?)γ≤α,φα,γ(1Tα,λ)=εΛγ,(εΛγshi Λαshang de chan wei ying she )(zhe shi gen ju (R1)you |Λα|=1).ze S(B)=∪α∈Y(Iα×Tα×Λα)guan yu er yuan yun suan (i,x,λ)(j,y,μ)-(<ψα,αβ(i,x)ψβ,αβ(j,y)>,xy,<φα,αβ(x,λ)φβ,αβ(y,μ)>).gou cheng yi ge LR-C-goodB-quasi-Ehresmannban qun ,ji zhong B=∪α∈Y(Iα×{1Tα} ×Λα).fan zhi ,mei ge LR-C-goodB-quasi-Ehresmannban qun dou ke ru ci gou zao .tui lun 3.2.4 she T=[Y;Tα]shi yi ge C-Ehresrmannban qun ,I=[Y;Iα]shi yi ge zuo zheng ze dai ju Λ=[Y;Λα]shi yi ge you zheng ze dai .re ying she ξ:∪α∈Y(Iα × Tα)→τl(I),(i,x)→(i,x)#η:∪α∈Y(Tα × Λα)→τr(Λ),(x,λ)→(x,λ)*man zu xia lie tiao jian :(L1)re (i,x)∈ Iα×Tαju j∈I3，ze (i,x)#j∈Iαβ:(R1)re (x,λ)∈Tα× Λα.ju μ ∈ Λβ,ze μ(x,λ)*Λαβ;(L2)zai (L1)zhong ,re α≤β,ze (i,x)#j=i;(R2)zai (R1)zhong ,re α ≤β,ze μ(x,λ)*=λ:(L3)re (i.x)Iα × Tαju (j,y)∈Iβ× Tβze (i,x)#(j,y#=((i,x)#j,xy)#;(R3)re (x,λ)∈Tα×Λαju (y,μ)∈Tβ×Λβ.ze (x,λ)*(y,μ)*=(xy,λ(y,μ)*)*;(P)re i∈Iα,λ ∈Λα,ze (?)β≤α,(?)j∈I3,(i,1Tα)#j=j(zhe shi gen ju (L2)you |Iα|=1)huo (?)β≤ α,∈ μ(1Tα,λ)*=μ(zhe shi gen ju (R2)you |Aα|=1).ze S(B)er ∪α∈Y(Iα × Tα × Aα)guan yu er yuan yun suan (i,x,λ)(j,y,μ)=((i,x)#j,xy,λ(y,μ)*)gou cheng yi ge LR-C-Ehresmann,,ji zhong B=Uα∈Y(Iα × {1Tα} × Aα).fan zhi ,mei ge LR-C-Ehresmannnban qun dou ke ru ci gou zao .tui lun 3.2.5 she T=[Y;Tα]shi yi ge C-Ehmannban qun ,dui yu (?)α∈Y,Iαhe Λαshi liang ge fei kong ji ge ju Iα ∩Iβ=(?)=Λα ∩ Λ3(α≠β).zuo zhi ji Pα=Iα × Tα.he Qα=Tα×Λα(α∈S).ji S=∪α∈Y(Iα ×Tα×Λα)ju B=∪α∈Y(Iα×{1Tα}×Λα).dui (?)α,γ∈Y，γ≤ αshi ,she ying she ψα,γ：Pα→τl(Iγ),(i,x)→ψα,γ(i,x)φα,γ→τr(Λγ),(x,λ)→φα,γ(x,λ)man zu xia lie tiao jian :(L1)re (i,x)∈Pαju j∈Iα,ze ψα,α(i,x)j=i;(R1)re (x,λ)∈ Qαju μ∈Λα,ze μφα,α(x,λ)=λ;(L2)re (i,x)∈&ju (j,y)∈Pβ ze ψα,αβ(i,x)ψβ,αβ(j,y)=ψα,αβ(i,x)ψβαβ(j,y)〉;(R2)re (x,λ)∈ Qαju (y,μ)∈Qβ,ze φα,αβ(x,λ)φβ,αβ(y,μ)=φα,αβ(x,λ)φβ,αβ(y,μ)〉(L3)re zai (L2)zhong ,δ≤αβ,ze ψα,βδ(k,xy)=ψα,δ(i,x)ψβ,δ(j,y),ji zhong k=〈ψα,αβ(i,x)ψβ,αβ(j,y)〉;(R3)re zai (R2)zhong ,δ ≤αβ,ze φαβ,δ(xy,v)=φα,δ(x,λ)φβ,δ(y,μ),ji zhong v=〈φα,αβ(x,λ)φβ,αβ(y,μ)〉;(P)re i∈Iα,λ ∈Λα,ze (?)γ≤α,ψα,γ(i,1Tα)=εIγ,(εIγshi Iγshang de heng deng ying she )(zhe shi gen ju (La)you |Iα|=1)huo (?)γ≤α,=∈Λγ,(∈Λγshi Λγshang de chan wei ying she )(zhe shi gen ju (R1)you |Λα|=1).ze S(B)=UαY,(Jα × Tα × Λα)guan yu er yuan yun suan (i,x,λ)(j,y,μ(〈ψα,αβ(i,x)ψβ,αβ(j,y),xy,〈φα,αβ(x,λ)〉,xy〈φα,αβ(x,λ)φβ,αβ(y,μ)〉)gou cheng yi ge LR-C-Ehresmannban qun ,ji zhong B=∪α∈Y(Iα×{1Tα}×Λα).fan zhi ,mei ge LR-C-Ehresmannban qun dou ke ru ci gou zao .
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