模糊拓扑空间中Q-紧集的非标准刻画

摘要

The nonstandard characterization of Q-compact set in fuzzy topological spaces is discussed in nonstandard enlarged model. Firstly, fuzzy sets are extended to nonstandard fuzzy sets, and the monad of fuzzy point is defined based on quasi-neighborhoods. Then, the nonstandard characterization of Q-compact set is Obtained by the monad, and the Q-compact spaces are non-standardly characterized. Finally, Tychonoff products theorem of Q-compact spaces is proved.%在非标准扩大模型下，讨论了模糊拓扑空间中Q-紧集的非标准刻画．首先，将模糊集合扩张为非标准模糊集合，借助模糊点的重域定义了模糊点的单子．其次，以模糊点的单子为工具，给出了Q-紧集的非标准刻画，并在此基础上得到了Q-紧空间的非标准刻画．最后，证明了Q-紧空间的Tychonoff乘积定理．