L-双拓扑空间的弱超仿紧性
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摘要
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.
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.
引文
[1]刘红平,孟广武.L-双拓扑空间中的*-配仿紧性[J].山东大学学报,2008,43(4):42-46.
[2]许浩,孟广武.L-双拓扑空间的D_α-层连通性[J].聊城大学学报,2010,23(2):8-12.
[3]薛艳霞,斯钦孟克,王瑞英.Fuzzy双拓扑空间中的拟开集和拟连续[J].内蒙古师范大学学报,2010,39(3):242-246.
[4]王小霞,姜金平.L-双拓扑空间中的配超紧性[J].模糊系统与数学,2011,25(3):62-66.
[5]王小霞,姜金平.L-双拓扑空间中几类弱连通集及其性质[J].贵州大学学报,2013,30(4):4-6.
[6]王冰,孟凡友.点式模糊化拟一致结构诱导的双拓扑[J].数学的实践与认识,2013,43(13):221-224.
[7]姜金平.L-双拓扑空间中的可数配超紧性[J].模糊系统与数学.2015,29(3):75-78.
[8]阮蒙蒙,王小霞.L-双拓扑空间的相对配仿紧性[J].江西科学,2018,36(4):570-572.
[9]王国俊.拓扑空间论[M].西安:陕西师范大学出版社,1988.
[2]许浩,孟广武.L-双拓扑空间的D_α-层连通性[J].聊城大学学报,2010,23(2):8-12.
[3]薛艳霞,斯钦孟克,王瑞英.Fuzzy双拓扑空间中的拟开集和拟连续[J].内蒙古师范大学学报,2010,39(3):242-246.
[4]王小霞,姜金平.L-双拓扑空间中的配超紧性[J].模糊系统与数学,2011,25(3):62-66.
[5]王小霞,姜金平.L-双拓扑空间中几类弱连通集及其性质[J].贵州大学学报,2013,30(4):4-6.
[6]王冰,孟凡友.点式模糊化拟一致结构诱导的双拓扑[J].数学的实践与认识,2013,43(13):221-224.
[7]姜金平.L-双拓扑空间中的可数配超紧性[J].模糊系统与数学.2015,29(3):75-78.
[8]阮蒙蒙,王小霞.L-双拓扑空间的相对配仿紧性[J].江西科学,2018,36(4):570-572.
[9]王国俊.拓扑空间论[M].西安:陕西师范大学出版社,1988.