Pointwise k -Pseudo Metric Space

Yu Zhong, Alexander Šostak and Fu-Gui Shi
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Yu Zhong: College of Science, North China University of Technology, Beijing 100144, China
Alexander Šostak: Department of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, Latvia
Fu-Gui Shi: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2021, vol. 9, issue 19, 1-15

Abstract: In this paper, the concept of a k -(quasi) pseudo metric is generalized to the L -fuzzy case, called a pointwise k -(quasi) pseudo metric, which is considered to be a map d : J ( L X ) × J ( L X ) ? [ 0 , ? ) satisfying some conditions. What is more, it is proved that the category of pointwise k -pseudo metric spaces is isomorphic to the category of symmetric pointwise k -remote neighborhood ball spaces. Besides, some L -topological structures induced by a pointwise k -quasi-pseudo metric are obtained, including an L -quasi neighborhood system, an L -topology, an L -closure operator, an L -interior operator, and a pointwise quasi-uniformity.

Keywords: pointwise k -(quasi) pseudo metric; pointwise k -remote neighborhood ball system; L -quasi neighborhood system; L -topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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