On The Completion of Hausdorff Topological Vector Spaces Using Nets

Authors

  • Adel Bashir Badi قسم الرياضيات، كلية العلوم، جامعة مصراتة

Keywords:

Topological vector spaces, Cauchy nets, Directed sets, Convergence, Completion, Nets, Subnets

Abstract

This paper contains a direct proof of the result asserting that every Hausdorff topological vector space has a completion. The proof here is different from known proofs of this result, since it uses only the convergence of nets and their basic properties. The completion is constructed as equivalence classes of Cauchy sequences

References

Jarchow, H., Locally Convex Spaces, 1981, B. G. Teubner, Stuttgart.

Narici, L. and Beckenstein, E., Topological Vector Spaces, 2^nd ed., 2011, CRC press.

Robertson, A. P. and Robertson W., Topological Vector Spaces, 2^nd ed., 1973, Cambredge university press.

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Published

2024-01-25

How to Cite

Badi, A. B. (2024). On The Completion of Hausdorff Topological Vector Spaces Using Nets. Journal of Academic Research, 13. Retrieved from https://lam-journal.ly/index.php/jar/article/view/150

Issue

Vol. 13 (2019)

Section

Basic Sciences

License

Copyright (c) 2024 عادل بشير بادي

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.