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.
Received: 04 September 2016
Published: 07 April 2018
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.
