ACADSTAFF UGM
| Title | : | Characterizations of Pointwise Pseudometrics via Pointwise Closed-Ball Systems |
| Author | : |
Chong Shen (1) Yi Shi (2) Fu-Gui Shi (3) Hadrian Andradi, M.Sc., Ph.D. (4) |
| Date | : | 5 2022 |
| Keyword | : | L -fuzzy number, L-fuzzy real line, L-topology, pointwise closed-ball system, pointwise pseudoquasi-metric L -fuzzy number, L-fuzzy real line, L-topology, pointwise closed-ball system, pointwise pseudoquasi-metric |
| Abstract | : | Pointwise pseudoquasi-metrics play an important role in the theory of lattice-valued topology ( L -topology). Bearing in mind that closed balls and their relations with pseudoquasi-metrics have historically attracted the attention of mathematicians, it is very surprising that no attention has been paid to the relations between pointwise pseudoquasi-metrics and closed balls. In this article, we first introduce the concept of pointwise closed-ball systems and prove that the eesulting category is isomorphic to that of pointwise pseudoquasi-metrics. Subsequently, we study the topological properties of pointwise pseudoquasi-metrics via pointwise closed-ball systems. Interestingly, the L -topologies defined by open sets and complements of closed sets coincide for any pointwise pseudometric. Finally, we expose an important theoretical application of the pointwise closed-systems in providing a different and relatively simpler proof of the celebrated metrization theorem of the L -fuzzy real line. |
| Group of Knowledge | : | Matematika |
| Original Language | : | English |
| Level | : | Internasional |
| Status | : |
Published
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