Completeness of fuzzy quasi-pseudometric spaces

Year 2023, Volume: 52 Issue: 2, 426 - 444, 31.03.2023

Shi Yi , Wei Yao

https://doi.org/10.15672/hujms.1082134

Abstract

The purpose of this paper is to present the relations among the completeness of sequences, of filters and of nets in the framework of fuzzy quasi-pseudometric spaces. In particular, we show that right completeness of filters and of sequences are equivalent under special conditions of fuzzy quasi-pseudometrics. By introducing a kind of more general right K-Cauchy nets in fuzzy quasi-pseudometric spaces, the equivalence between the completeness of the nets and the sequential completeness is established.

Keywords

Fuzzy quasi-pseudometric space, Cauchy sequence, Cauchy filter, Cauchy net, completeness

Supporting Institution

National Natural Science Foundation of China

Project Number

11871189

Thanks

This paper is supported by National Natural Science Foundation of China (11871189, 1211101082), Natural Science Foundation of Hebei Province (A2020208008), Jiangsu Provincial Innovative and Entrepreneurial Talent Support Plan (JSSCRC202521) and the Startup Foundation for Introducing Talent of NUIST (2019r63).

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