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广义近似空间的拓扑分离性与紧性

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本文对一般广义近似空间(U,R)进行了拓扑式研究,利用R-开集概念诱导了广义近似空间对应的拓扑空间,并利用诱导的拓扑空间定义了相应广义近似空间的T0性与T1性及拓扑紧性.证明了广义近似空间的T0性强于Ta0性,T1性与Ta1性等价;证明了广义近似空间的关系紧性强于拓扑紧性,并用反例说明了关于分离性和紧性其他不能蕴含的情形.
Topological Separation Axioms and Compactness of Generalized Approximation Spaces
Generalized approximation spaces are studied from topological point of view.In terms of induced topologies defined by R-open sets,some new separation axioms T0,T1,and topological compactness of generalized approximation spaces are introduced.It is proved that T0 separation axiom is stronger than Ta0,while T1 is equivalent to Ta1 of generalized approximation spaces.It is also proved that relational compactness is stronger than topological compactness for generalized approximation spaces.Some examples are constructed to illustrate distinctions between some separation axioms,and reveal that topological compactness does not imply relational compactness of generalized approximation spaces.

Generalized Approximation SpaceRough SetInduced TopologySeparation AxiomTopological Compactness

荣宇音、徐罗山

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扬州大学数学科学学院,江苏扬州 225002

广义近似空间 粗糙集 诱导拓扑 分离性 拓扑紧性

国家自然科学基金资助项目国家自然科学基金资助项目江苏省高校自然科学基金资助项目江苏高校品牌专业建设工程项目扬州大学大学生学术科技创新基金资助项目

116710086147234315KJD110006PPZY2015B109

2017

模糊系统与数学
国防科技大学理学院

模糊系统与数学

CSTPCD北大核心
影响因子：0.42
ISSN：1001-7402
年,卷(期)：2017.31(5)
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