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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Characterizations of \(\alpha \)-Quasi Uniformity and Theory of \(\alpha \)-P.Q. Metrics
verfasst von : Xiu-Yun Wu, Li-Li Xie, Shi-Zhong Bai
Erschienen in: Fuzzy Information & Engineering and Operations Research & Management
Verlag: Springer Berlin Heidelberg
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Abstract
In Wu Fuzzy Systems and Mathematics 3:94–99, 2012, the author introduced concepts of \(\alpha \)-remote neighborhood mapping and \(\alpha \)-quasi uniform, and obtained many good results in \(\alpha \)-quasi uniform spaces. This chapter will further investigate properties of \(\alpha \)-remote neighborhood mapping, and give some characterizations of \(\alpha \)-quasi uniforms. Based on this, this chapter also introduces concept of \(\alpha \)-P.Q. metric, and establishes the relations between \(\alpha \)-quasi uniforms and \(\alpha \)-P.Q. metrics.