On covering properties of end and ray spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915737411518464 |
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| author | Carvalho, Rodrigo Rey Duzi, Matheus Rodrigues, Vinicius de Oliveira |
| author_facet | Carvalho, Rodrigo Rey Duzi, Matheus Rodrigues, Vinicius de Oliveira |
| contents | We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindelöf degree, the extent, the Rothberger property, $σ$-compactness and the Menger property for ray, end and edge-end spaces. We show that $σ$-compactness and the Menger property are equivalent for these spaces, and that they are all $D$-spaces. As an application of some of these characterizations, we are able to provide combinatorial characterizations of graphs with countably many ends and edge-ends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On covering properties of end and ray spaces Carvalho, Rodrigo Rey Duzi, Matheus Rodrigues, Vinicius de Oliveira Combinatorics General Topology 05C63, 54D20, 06A07, 54D45 We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindelöf degree, the extent, the Rothberger property, $σ$-compactness and the Menger property for ray, end and edge-end spaces. We show that $σ$-compactness and the Menger property are equivalent for these spaces, and that they are all $D$-spaces. As an application of some of these characterizations, we are able to provide combinatorial characterizations of graphs with countably many ends and edge-ends. |
| title | On covering properties of end and ray spaces |
| topic | Combinatorics General Topology 05C63, 54D20, 06A07, 54D45 |
| url | https://arxiv.org/abs/2510.10825 |