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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 2

A lexicographical order induced by Schauder bases

Neşet Özkan Tan
Pages
511–515
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Indeed, this order can be considered as a lexicographical order since it is a generalization of lexicographical order in $\mathbb{R}^{n}.$ We also provide order structural properties of the order by approaching geometrical (cone) sense.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we show that every Banach space with a Schauder basis can be seen as a totally ordered vector space.
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Key Findings & Data:In this paper, we show that every Banach space with a Schauder basis can be seen as a totally ordered vector space.
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Conclusion & Impact:Indeed, this order can be considered as a lexicographical order since it is a generalization of lexicographical order in $\mathbb{R}^{n}.$ We also provide order structural properties of the order by approaching geometrical (cone) sense.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:total order · cone · Schauder basis

Abstract

In this paper, we show that every Banach space with a Schauder basis can be seen as a totally ordered vector space. Indeed, this order can be considered as a lexicographical order since it is a generalization of lexicographical order in $\mathbb{R}^{n}.$ We also provide order structural properties of the order by approaching geometrical (cone) sense.

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Cite This Article

Tan, N. Ö. (2022). A lexicographical order induced by Schauder bases. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 2, 511–515. https://ajindex.com/articles/529519

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