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ON THE COMPLETION OF $b$-METRIC SPACES

Part of: Spaces with richer structures

Published online by Cambridge University Press:  05 July 2018

NGUYEN VAN DUNG Open the ORCID record for NGUYEN VAN DUNG [Opens in a new window]  and
VO THI LE HANG Open the ORCID record for VO THI LE HANG [Opens in a new window]
NGUYEN VAN DUNG*
Affiliation:
Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam email nguyenvandung2@tdt.edu.vn
VO THI LE HANG
Affiliation:
Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam email vtlhang@dthu.edu.vn
*
✉nguyenvandung2@tdt.edu.vn
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Abstract

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Based on the metrisation of $b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’, Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every $b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a $b$-metric space.

Keywords

metric spaceb-metriccompletion

MSC classification

Primary: 54E50: Complete metric spaces
Secondary: 54E25: Semimetric spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 298 - 304
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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