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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.00301 |
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| _version_ | 1866913837296386048 |
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| author | Zabeti, Omid |
| author_facet | Zabeti, Omid |
| contents | Suppose $Σ$ is a topological space and $S(Σ)$ is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of $Σ$. In this paper, we establish some lattice and topological aspects of $S(Σ)$. In particular, as an application, we show that the unbounded order convergence and the order convergence are stable under passing to the Fremlin tensor product of two Archimedean vector lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fremlin tensor product behaves well with the unbounded order convergence Zabeti, Omid Functional Analysis Suppose $Σ$ is a topological space and $S(Σ)$ is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of $Σ$. In this paper, we establish some lattice and topological aspects of $S(Σ)$. In particular, as an application, we show that the unbounded order convergence and the order convergence are stable under passing to the Fremlin tensor product of two Archimedean vector lattices. |
| title | Fremlin tensor product behaves well with the unbounded order convergence |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2309.00301 |