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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (3): 315-320    
    
广义近似空间的粗糙同胚与拓扑同胚
荣宇音, 徐罗山
扬州大学 数学科学学院, 江苏扬州 225002
Rough homeomorphisms and topological homeomorphisms of generalized approximation spaces
RONG Yu-yin, XU Luo-shan
Department of Mathematics, Yangzhou University, Yangzhou 225002, China
 全文: PDF 
摘要： 对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性, 探讨了他们的性质及相互关系. 证明了两个粗糙连续映射的复合还是粗糙连续的, 每个粗糙连续的映射都是拓扑连续的. 在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念, 证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性.
关键词： 广义近似空间;  粗糙集;  诱导拓扑;  粗糙连续;  粗糙同胚    
Abstract: This paper introduces and characterizes rough continuity and topological continuity of maps between generalized approximation spaces. Properties and relationships of rough continuity and topological continuity are considered. It is proved that compositions of rough continuous maps are also rough continuous, and every rough continuous map is topological continuous. With these two continuities, concepts of rough homeomorphism properties and topological homeomorphism properties are defined. It is proved that every topological homeomorphism property is a rough homeomorphism property. Besides, some properties such as separation axioms, connectedness and compactness of generalized approximation spaces are shown to be rough or topological homeomorphism properties.
Key words: generalized approximation space    rough set    induced topology    rough continuity    rough homeomorphism
收稿日期: 2016-09-04 出版日期: 2018-04-07
:  O153.1  
基金资助: 国家自然科学基金资助项目(11671008, 61472343); 江苏省高校自然科学基金(15KJD110006); 江苏高校品牌专业建设工程(PPZY2015B109); 扬州大学大学生科技创新基金
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荣宇音
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引用本文:

荣宇音, 徐罗山. 广义近似空间的粗糙同胚与拓扑同胚[J]. 高校应用数学学报, 2017, 32(3): 315-320.

RONG Yu-yin, XU Luo-shan. Rough homeomorphisms and topological homeomorphisms of generalized approximation spaces. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 315-320.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I3/315

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