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Open AccessArticle

Completeness in Quasi-Pseudometric Spaces—A Survey

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400 084 Cluj-Napoca, Romania
Mathematics 2020, 8(8), 1279; https://doi.org/10.3390/math8081279
Received: 17 June 2020 / Revised: 22 July 2020 / Accepted: 24 July 2020 / Published: 3 August 2020
The aim of this paper is to discuss the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right K-Cauchy net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R. A. Stoltenberg, Proc. London Math. Soc. 17 (1967), 226–240, and V. Gregori and J. Ferrer, Proc. Lond. Math. Soc., III Ser., 49 (1984), 36. A discussion on nets defined over ordered or pre-ordered directed sets is also included. View Full-Text
Keywords: metric space; quasi-metric space; uniform space; quasi-uniform space; Cauchy sequence; Cauchy net; Cauchy filter; completeness metric space; quasi-metric space; uniform space; quasi-uniform space; Cauchy sequence; Cauchy net; Cauchy filter; completeness
MDPI and ACS Style

Cobzas, Ş. Completeness in Quasi-Pseudometric Spaces—A Survey. Mathematics 2020, 8, 1279. https://doi.org/10.3390/math8081279

AMA Style

Cobzas Ş. Completeness in Quasi-Pseudometric Spaces—A Survey. Mathematics. 2020; 8(8):1279. https://doi.org/10.3390/math8081279

Chicago/Turabian Style

Cobzas, Ştefan. 2020. "Completeness in Quasi-Pseudometric Spaces—A Survey" Mathematics 8, no. 8: 1279. https://doi.org/10.3390/math8081279

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