模糊拓扑空间中有限覆盖性质的非标准刻画

摘要

In nonstandard enlarged model, the nonstandard characterization of finite covering property is discussed in fuzzy topological spaces. Firstly, fuzzy sets are extended to nonstandard fuzzy sets, and the monad of fuzzy point is defined. Then, the nonstandard characterization of finite covering property is obtained by the monad, and the finite covering spaces are nonstandard characterized. Finally, Tychonoff-products theorem of finite covering spacess is proved by these nonstandard characterizations.%在非标准扩大模型下,讨论了模糊拓扑空间中有限覆盖性质的非标准刻画.将模糊集合扩张为非标准模糊集合,并定义了模糊点的单子.借助模糊点的单子给出了有限覆盖性质的非标准刻画,并在此基础上得到了有限覆盖空间的非标准刻画.证明了有限覆盖空间的Tychonoff乘积定理.