诱导空间的网权、Lindelof度与胞腔度

Net weight, Lindelōf degree and cellularity of induced spaces

在一般Fuzzy格L中引入了网权、Lindelǒf度与胞腔度的概念。讨论了诱导空间(L^x,ω_L)的网权、Lindelǒf度、胞腔度与生成它的分明拓扑空间(X,)的网权、Lindelǒf度、胞腔度之间的关系。证明了(L^x,ω_L)的网权等于(X,)的网权与Fuzzy格L的网权的乘积,(L^x,ω_L)的Lindelǒf度大于或等于(X,)的Lindelǒf度与Fuzzy格L的Lindelǒf度的乘积,小于或等于(X,)的Lindelǒf度与Fuzzy格L的势的乘积。当L是正则格时,(L^x,ω_L)的胞腔度等于(X,)的胞腔度。

The notions of net weight, Lindelǒf degree and cellularity on fuzzy lattice L are introduced. The relations between net weight, Lindelǒf degree and cellularity of induced spaces (L^X, ω_(J)) and that of their generated spaces(X, J) are discussed, that the net weight of (L^X, ω_L(J)) equals the product of net weights of (X, J) and L, the Lindelf degree of (L^X, ω_L(J)) is bigger than the product of Lindelóf degrees of (X, J) and L, smaller than the product of Lindelǒf degree of (X, J) and cardinanity of L are proved. For a regular Lattice L, that the cellularity of (L^X, ω_L(J)) equals the cellularity of (X, J) is proved as well.