{"title":"On an Open Problem for Definable Subsets of Covering Approximation Spaces","authors":"Mei He, Ying Ge, Jingyu Qian","country":null,"institution":"","volume":51,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":511,"pagesEnd":514,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/7038","abstract":"Let (U;D) be a Gr-covering approximation space\r\n(U; C) with covering lower approximation operator D and covering\r\nupper approximation operator D. For a subset X of U, this paper\r\ninvestigates the following three conditions: (1) X is a definable subset\r\nof (U;D); (2) X is an inner definable subset of (U;D); (3) X is an\r\nouter definable subset of (U;D). It is proved that if one of the above\r\nthree conditions holds, then the others hold. These results give a\r\npositive answer of an open problem for definable subsets of covering\r\napproximation spaces.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 51, 2011"}