A topological characterization of end space of infinite graphs via games, subspaces and products
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910145632534528 |
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| author | Aurichi, Leandro Boska, Gustavo Giacopello, Davide Júnior, Paulo Magalhães |
| author_facet | Aurichi, Leandro Boska, Gustavo Giacopello, Davide Júnior, Paulo Magalhães |
| contents | In 1992, Diestel asked which topological spaces could be represented as the end space of some graph. In 2023, Pitz provided a solution to this question by giving a topological characterization of end spaces using a hereditarily complete special subbase. In this paper, we present an alternative topological characterization of end spaces, in which we employ a special subbase and a topological game. Furthermore, we provide several applications of this characterization: we show that every end space is hereditarily Baire, that $G_δ$ subspaces of end spaces are also end spaces, and that the product of end spaces is not always an end space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A topological characterization of end space of infinite graphs via games, subspaces and products Aurichi, Leandro Boska, Gustavo Giacopello, Davide Júnior, Paulo Magalhães General Topology Combinatorics 05C63 05C05 05C40 In 1992, Diestel asked which topological spaces could be represented as the end space of some graph. In 2023, Pitz provided a solution to this question by giving a topological characterization of end spaces using a hereditarily complete special subbase. In this paper, we present an alternative topological characterization of end spaces, in which we employ a special subbase and a topological game. Furthermore, we provide several applications of this characterization: we show that every end space is hereditarily Baire, that $G_δ$ subspaces of end spaces are also end spaces, and that the product of end spaces is not always an end space. |
| title | A topological characterization of end space of infinite graphs via games, subspaces and products |
| topic | General Topology Combinatorics 05C63 05C05 05C40 |
| url | https://arxiv.org/abs/2604.17164 |