Hyperspace Selections Avoiding Points
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909076878786560 |
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| author | Gutev, Valentin |
| author_facet | Gutev, Valentin |
| contents | In this paper, we deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case -- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic order, and gives a characterisation of the so called weakly cyclically orderable spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06979 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hyperspace Selections Avoiding Points Gutev, Valentin General Topology 54B20, 54C65, 54D05, 54D30, 54F05, 54F65 In this paper, we deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case -- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic order, and gives a characterisation of the so called weakly cyclically orderable spaces. |
| title | Hyperspace Selections Avoiding Points |
| topic | General Topology 54B20, 54C65, 54D05, 54D30, 54F05, 54F65 |
| url | https://arxiv.org/abs/2110.06979 |