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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2309.01349 |
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| _version_ | 1866911845525225472 |
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| author | Iwamoto, Yutaka |
| author_facet | Iwamoto, Yutaka |
| contents | We study the space $H(\SO)$ of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line $\HH=[0,\infty)$. In contrast to the case of homomorphisms of uniformly continuous functions, it is shown that a homomorphism in $H(\SO)$ which maps the unit to zero must be zero-homomorphism. Consequently, we show that the space $H(\SO)$ without zero-homomorphism is homeomorphic to $\HH\times (0, \infty)$. By describing a neighborhood base of zero-homomorphism, we show that $H(\SO)$ is homeomorphic to the space $\HH\times (0, \infty)$ with one point added. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01349 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homomorphisms of the lattice of slowly oscillating functions on the half-line Iwamoto, Yutaka General Topology Functional Analysis 46E05, 54C35 We study the space $H(\SO)$ of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line $\HH=[0,\infty)$. In contrast to the case of homomorphisms of uniformly continuous functions, it is shown that a homomorphism in $H(\SO)$ which maps the unit to zero must be zero-homomorphism. Consequently, we show that the space $H(\SO)$ without zero-homomorphism is homeomorphic to $\HH\times (0, \infty)$. By describing a neighborhood base of zero-homomorphism, we show that $H(\SO)$ is homeomorphic to the space $\HH\times (0, \infty)$ with one point added. |
| title | Homomorphisms of the lattice of slowly oscillating functions on the half-line |
| topic | General Topology Functional Analysis 46E05, 54C35 |
| url | https://arxiv.org/abs/2309.01349 |