L-双拓扑空间的弱超仿紧性

Weakly ultra-paraompactness in L-bitopological spaces

将L-拓扑空间的超仿紧性引入L-双拓扑空间,探讨L-双拓扑空间的弱超仿紧性。基于远域族、余有限等概念,采用分析和归纳的方法,在L-双拓扑空间中定义了弱超仿紧集、双弱超仿紧集、弱配仿紧集等,证明了弱配超仿紧的L-双拓扑空间一定是弱配仿紧的L-双拓扑空间。研究表明,弱配超仿紧性和弱配仿紧性具闭遗传性。在同胚的L值Zadeh函数作用下,弱配超仿紧集的像一定也是弱配超仿紧集,即弱配超仿紧性具弱拓扑不变性。该结果为L-拓扑空间的超仿紧性理论研究提供了借鉴。

This paper discusses the weak ultra-paraompactness of the L-bitopological space by introducing the ultra-paraompactness of the L-topological space into the L-bitopological space. The study building on the relative R-neighborhood and surplus limited set is focused on the definition of weakly ultra-paraompacted set,double weakly ultra-paraompacted set and weakly pairwise ultra-paraompacted set using the analytical and inductive methods,proving that weakly pairwise ultra-paraompacted L-bitopological space is weakly ultra-paraompacted L-bitopological space. The results show that weakly pairwise ultraparaompactness and weakly pairwise paraompactness are closed hereditary;under the action of the value of the homeomorphic L-Zadeh function,the image of the pairwise ultra-paraompacted set must also be a pairwise ultra-paraompacted set,meaning that weakly pairwise ultra-paraompactness is weakly topological properties. This result could provide a reference for the study of ultra-paraompactness theory of topological space.