| The Closeness of the $\tau$-Standard Part of a Set |
| Received:March 26, 2009 Revised:January 18, 2010 |
| Key Words:
enlarged models saturated models $\tau$-standard part $\tau$-closed set.
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| Fund Project:Supported by the Natural Science Foundation of Shaanxi Province (Grant No.2007A12) and the Youth Science and Technology Foundation of Xi'an University of Architecture and Technology (Grant Nos.QN0736; QN0833). |
| Author Name | Affiliation | | Dong Li CHEN | School of Science, Xi'an University of Architecture and Technology, Shaanxi 710055, P. R. China | | Jing Jing FENG | School of Science, Xi'an University of Architecture and Technology, Shaanxi 710055, P. R. China
Department of Basic Courses, Xi'an Peihua University, Shaanxi 710125, P. R. China | | Chun Hui MA | School of Science, Xi'an University of Architecture and Technology, Shaanxi 710055, P. R. China |
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| Abstract: |
| In this paper, the closeness of the $\tau$-standard part of a set is discussed. Some related propositions of the $\tau$-neighborhood system of a set are given. And then some related conclusions of the $\tau$-monad of a set and the $\tau$-standard part of a set are presented. And based on it, the necessary and sufficient conditions of the enlarged model and the saturated model are showed. Finally, some sufficient conditions that the $\tau$-standard part of a set is closed are proved in the enlarged model and the saturated model. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.023 |
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