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浙江大学学报(理学版)  2018, Vol. 45 Issue (4): 409-412    DOI: 10.3785/j.issn.1008-9497.2018.04.005
数学与计算机科学     
由度量空间诱导的*-拓扑和s-拓扑Ts
史艳维1, 马春晖2
1. 西安培华学院 智能科学与信息工程学院, 陕西 西安 710125;
2. 西安建筑科技大学 理学院, 陕西 西安 710055
*-Topology T* and s-topology Ts induced by metric space
SHI Yanwei1, MA Chunhui2
1. School of Intelligent Science and Information Engineering, Xi'an Peihua University, Xi'an 710125, China;
2. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China
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摘要: 在多饱和模型下研究了由度量空间诱导的*-拓扑T*s-拓扑Ts.首先,为了构造*-拓扑T*,提出了有限点集的概念.其次,在此拓扑空间中证明了每个内集是紧集,每个开集是饱和集,以及标准部分映射是连续映射.最后,在s-拓扑Ts中讨论了闭包算子、内部算子和*映射.
关键词: 有限点饱和集标准部分映射函子    
Abstract: This paper studies *-topology T* and s-topology Ts in polysaturated nonstandard model, which are induced by metric space on two nonstandard sets. In order to construct *-topology T*, the set of finite points is introduced. It shows that every internal set is compact, every open set is saturated and standard part mapping is continuous. Finally, the closure operator, interior operator and mapping * are discussed under s-topology Ts.
Key words: finite point    saturated set    standard part mapping    functor
收稿日期: 2017-09-30 出版日期: 2018-07-12
CLC:  O189  
基金资助: Supported by Scientific Research Project of Xi'an Peihua University (PHKT17001) and Basic Research Fund of Xi'an University of Architecture and Technology(JC1709)
作者简介: 史艳维(1980-),ORCID:http://orcid.org/0000-0001-6056-3014,female,master,associate professor,the fields of interest are general topology and nonstandard analysis,E-mail:shi_yanwei@163.com.
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引用本文:

史艳维, 马春晖. 由度量空间诱导的*-拓扑和s-拓扑Ts[J]. 浙江大学学报(理学版), 2018, 45(4): 409-412.

SHI Yanwei, MA Chunhui. *-Topology T* and s-topology Ts induced by metric space. Journal of Zhejiang University (Science Edition), 2018, 45(4): 409-412.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.04.005        https://www.zjujournals.com/sci/CN/Y2018/V45/I4/409

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