广义近似空间的粗糙同胚与拓扑同胚

Rough homeomorphisms and topological homeomorphisms of generalized approximation spaces

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.

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 axe shown to be rough or topological homeomorphism properties.