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Pointwise k-Pseudo Metric Space

Alexander ŠOstakFu-gui ShiYu Zhong

subject

PointwisePure mathematicsGeneral Mathematicspointwise <i>k</i>-(quasi) pseudo metricComputer Science::Digital Libraries<i>L</i>-quasi neighborhood systemMetric spaceOperator (computer programming)Metric (mathematics)Computer Science (miscellaneous)QA1-939<i>L</i>-topologyBall (mathematics)pointwise <i>k</i>-remote neighborhood ball systempointwise <i>k</i>-(quasi) pseudo metric; pointwise <i>k</i>-remote neighborhood ball system; <i>L</i>-quasi neighborhood system; <i>L</i>-topologyEngineering (miscellaneous)MathematicsMathematics

description

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(LX)×J(LX)⟶[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.

yearjournalcountryeditionlanguage
2021-10-01Mathematics
10.3390/math9192505https://www.mdpi.com/2227-7390/9/19/2505