Dense and subspace dense subsets in finite-dimensional spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910427535900672 |
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| author | Herzi, Salah Marzougui, Habib |
| author_facet | Herzi, Salah Marzougui, Habib |
| contents | This note is motivated by the article of Bamerni, Kadets and Kiliçman [J. Math. Anal. Appl. 435 (2), 1812--1815 (2016)]. We consider the remaining problem which claims that if $A$ is a dense subset of a finite dimensional space $X$, then there is a nontrivial subspace $M$ of $X$ such that $A\cap M$ is dense in $M$. We show that the above problem has a negative answer when $X=\mathbb{K}^{n}$ ($\mathbb{K}= \mathbb{R}$ or $\mathbb{C}$) for every $n\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01372 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dense and subspace dense subsets in finite-dimensional spaces Herzi, Salah Marzougui, Habib Functional Analysis 47A16-47A15 This note is motivated by the article of Bamerni, Kadets and Kiliçman [J. Math. Anal. Appl. 435 (2), 1812--1815 (2016)]. We consider the remaining problem which claims that if $A$ is a dense subset of a finite dimensional space $X$, then there is a nontrivial subspace $M$ of $X$ such that $A\cap M$ is dense in $M$. We show that the above problem has a negative answer when $X=\mathbb{K}^{n}$ ($\mathbb{K}= \mathbb{R}$ or $\mathbb{C}$) for every $n\geq 2$. |
| title | Dense and subspace dense subsets in finite-dimensional spaces |
| topic | Functional Analysis 47A16-47A15 |
| url | https://arxiv.org/abs/2108.01372 |