On The Completion of Hausdorff Topological Vector Spaces Using Nets

عادل بشير بادي

On The Completion of Hausdorff Topological Vector Spaces Using Nets

المؤلفون

عادل بشير بادي قسم الرياضيات، كلية العلوم، جامعة مصراتة

الكلمات المفتاحية:

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

الملخص

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

المراجع

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.

التنزيلات

pdf (English)

منشور

2024-01-25

كيفية الاقتباس

بادي ع. ب. (2024). On The Completion of Hausdorff Topological Vector Spaces Using Nets. مجلة البحوث الأكاديمية, 13. استرجع في من https://lam-journal.ly/index.php/jar/article/view/150