Completeness in Quasi-Pseudometric Spaces—A Survey

Ştefan Cobzas
Additional contact information
Ştefan Cobzas: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400 084 Cluj-Napoca, Romania

Mathematics, 2020, vol. 8, issue 8, 1-19

Abstract: 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.

Keywords: metric space; quasi-metric space; uniform space; quasi-uniform space; Cauchy sequence; Cauchy net; Cauchy filter; completeness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1279/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1279/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:8:p:1279-:d:393932

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().