Completeness of fuzzy quasi-pseudometric spaces

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

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