Hyperspaces of the double arrow
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913323643043840 |
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| author | Barría, Sebastián |
| author_facet | Barría, Sebastián |
| contents | Let $\mathbb{A}$ and $\mathbb{S}$ denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any $n\geq 1$, the space of all unions of at most $n$ closed intervals of $\mathbb{A}$ is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of $\mathbb{A}$ and $\mathbb{S}$ are homogeneous. This partially solves an open question of A. Arhangel'skiǐ. In contrast, we show that the space of closed intervals of $\mathbb{S}$ is homogeneous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperspaces of the double arrow Barría, Sebastián General Topology 54B20, 54B10, 54F05, 54A20, 54D30, 54E35 Let $\mathbb{A}$ and $\mathbb{S}$ denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any $n\geq 1$, the space of all unions of at most $n$ closed intervals of $\mathbb{A}$ is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of $\mathbb{A}$ and $\mathbb{S}$ are homogeneous. This partially solves an open question of A. Arhangel'skiǐ. In contrast, we show that the space of closed intervals of $\mathbb{S}$ is homogeneous. |
| title | Hyperspaces of the double arrow |
| topic | General Topology 54B20, 54B10, 54F05, 54A20, 54D30, 54E35 |
| url | https://arxiv.org/abs/2404.13741 |