L-Fuzzy拓扑空间中局部F紧性的可乘性

On the local F-Compactness in L-fuzzy product topological spaces

在文[9]中,作者提出了六种L—Fuzzy拓扑空间中的局部F紧性。即,强局部F紧性、星强局部F紧性,局部F紧性,星局部F紧性,弱局部F紧性和星弱局部F紧性。本文讨论了L-Fuzzy拓扑空间族的乘积空间(L^x,δ)的六种局部F紧性与其因子空间的相应局部F紧性之间的关系。证明了前四种局部F紧性是有限可乘性质,后两种局部F紧性是积稀有限可乘性质。最后给出了一类特殊空间是星局部F紧空间或星弱局部F紧空间的充要条件。

The paper [9] presented six kinds of the concept of the local F-compa- ctness in L-Fuzzy topological space, They have closed hereditary property and four of them have opened hereditary property. And they are weak topological invariant. This paper has proved that the strong local F-compactness, the star-strong local F-compactness, the local F-compactness and the star local F-compactness have limited product property. And also when the product space (L^X, δ)=(L^(X_t),δ_t) satisfy the condition: for every x_a∈M~*(L^X), x_a∈A_t, A_t∈δ(t∈T), exsit a t_0∈T, such that x_a≤A_(to), then if (L_(X_t), δ_t)(t∈T, |T|< +∞) is the star local F-compactness, or the star-strong local F-compactness so is their product space (L^x, δ).