Pointwise <i>k</i>-Pseudo Metric Space

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(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.

Keywords

• pointwise <i>k</i>-(quasi) pseudo metric
• pointwise <i>k</i>-remote neighborhood ball system
• <i>L</i>-quasi neighborhood system
• <i>L</i>-topology