Skip to main content
Log in

Some questions on partial metric spaces

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

We show that the completion of a partial metric space can fail be unique, which answers a question on completions of partial metric spaces. In addition, to this paper discusses metrizability around partial metric spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T Abdeljawad, E Karapinar, K Tas. A generalized contraction principle with control functions on partial metric spaces, Computers and Mathematics with Applications, 2012, 63(3): 716–719.

    Article  MathSciNet  Google Scholar 

  2. H Aydi, M Abbas, C Vetro. Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and its Applications, 2012, 159(4): 3234–3242.

    Article  MathSciNet  Google Scholar 

  3. T Banakh, V Bogachev, A Kolesnikov. k*-metrizable spaces and their applications, Journal of Mathematical Sciences, 2008, 155(4): 475–522.

    Article  MathSciNet  Google Scholar 

  4. M Bukatin, R Kopperman, S Matthews, H Pajoohesh. Partial metric spaces, American Mathematical Monthly, 2009, 116(8): 708–718.

    Article  MathSciNet  Google Scholar 

  5. N V Dung. On the completion of partial metric spaces, Quaestiones Mathematicae, 2017, 40(5): 589–597.

    Article  MathSciNet  Google Scholar 

  6. S P Franklin. Spaces in which sequences suffice, II, Fundamenta Mathematicae, 1967, 61: 51–56.

    Article  MathSciNet  Google Scholar 

  7. X Ge, S Lin. Completions of partial metric spaces, Topology and its Applications, 2015, 182: 16–23.

    Article  MathSciNet  Google Scholar 

  8. S Han, J Wu, D Zhang. Properties and principles on partial metric spaces, Topology and its Applications, 2017, 230: 77–98.

    Article  MathSciNet  Google Scholar 

  9. D Ilic, V Pavlovic, V Rakocevic. Extensions of the Zamfirescu theorem to partial metric spaces, Mathematical and Computer Modelling, 2012, 55(3–4): 801–809.

    Article  MathSciNet  Google Scholar 

  10. E Karapinar, I Erhan. Fixed point theorems for operators on partial metric spaces, Applied Mathematics Letters, 2011, 24(11): 1894–1899.

    Article  MathSciNet  Google Scholar 

  11. R Kopperman, S Matthews, H Pajoohesh. Completions of partial metrics into value lattices, Topology and its Applications, 2009, 156(8): 1534–1544.

    Article  MathSciNet  Google Scholar 

  12. H P Künzi, H Pajoohesh, M Schellekens. Partial quasi-metrics, Theoretical Computer Science, 2006, 365(3): 237–246.

    Article  MathSciNet  Google Scholar 

  13. S Leader, S Baron. Sequential topologies, American Mathematical Monthly, 1966, 73: 677–678.

    MathSciNet  Google Scholar 

  14. S Lin. A note on the Arens’ space and sequential fan, Topology and its Applications, 1997, 81(3): 185–196.

    Article  MathSciNet  Google Scholar 

  15. S Matthews. Partial metric topology, in General Topology and Applications: Eighth Summer Conference at Queens College 728(1992), G Itzkowitz et al, eds, Annals of the New York Academy of Sciences, New York, 1994: 183–197.

    Google Scholar 

  16. S Moshokoa. On the 0-Cauchy completion of a partial metric space, Turkish Journal of Mathematics and Computer Science, 2016, 4: 10–15

    Google Scholar 

  17. S Oltra, S Romaguera, E Sánchez-Pérez. Bicompleting weightable quasi-metric spaces and partial metric spaces, Rendiconti del Circolo Matematico di Palermo, 2002, 51: 151–162.

    Article  MathSciNet  Google Scholar 

  18. S O’Neill. Two Topologies are Better Than One, University of Warwick, Coventry, UK, 1995.

    Google Scholar 

  19. L Peng, Z Guo. A note on joint metrizability of spaces on families subspaces, Topology and its Applications, 2015, 188: 1–15.

    Article  MathSciNet  Google Scholar 

  20. S Shukla. Partial b-metric spaces and fixed point theorems, Mediterranean Journal of Mathematics, 2014, 11: 703–711.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shou Lin.

Additional information

This project is supported by the National Natural Science Foundation of China (11801254, 61472469, 11461005).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ge, X., Lin, S. Some questions on partial metric spaces. Appl. Math. J. Chin. Univ. 35, 392–398 (2020). https://doi.org/10.1007/s11766-020-3569-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-020-3569-z

Keywords

MR Subject Classification

Navigation