Topological structure of generalized rough sets

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• 作者：Zhaowen Li^a ; ^{lizhaowen8846@126.com} ; Tusheng Xie^b ; ^{tushengxie@126.com} ; Qingguo Li^c ; ^{liqingguo11@yahoo.cn}
• 关键词：Reflexive relations ; Tolerance relations ; Generalized rough sets ; Topological spaces ; Topological properties ; Approximating spaces
• 刊名：Computers and Mathematics with Applications
• 出版年：2012
• 期刊代码：37_08981221
• 类别：cp
• 出版时间：March, 2012
• 卷：63
• 期：6
• 页码：1066-1071
• 文件大小：209 K

摘要

In this paper, we investigate some properties of such as compactness, separate property, Lindel枚f property and connectedness, where is induced by a reflexive relation on which may be infinite. Moreover, we introduce the concept of approximating spaces and research their characterizations and properties. Particularly, we obtain a sufficient and necessary condition that topological spaces are approximating spaces. These will be not only conducive to better understanding basic concepts and properties of a rough set, but also have theory and actual significance to topology.