Two Selection Theorems for Extremally Disconnected Spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913978061422592 |
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| author | Gutev, Valentin |
| author_facet | Gutev, Valentin |
| contents | The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about extension of densely defined continuous selections for compact-valued continuous mappings, in fact a generalisation of this result to all usco mappings with a regular range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Selection Theorems for Extremally Disconnected Spaces Gutev, Valentin General Topology 54C10, 54C20, 54C60, 54C65, 54D35, 54G05 The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about extension of densely defined continuous selections for compact-valued continuous mappings, in fact a generalisation of this result to all usco mappings with a regular range. |
| title | Two Selection Theorems for Extremally Disconnected Spaces |
| topic | General Topology 54C10, 54C20, 54C60, 54C65, 54D35, 54G05 |
| url | https://arxiv.org/abs/2409.09490 |