A subbase property for describing edge-end spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916914469535744 |
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| author | Real, Lucas |
| author_facet | Real, Lucas |
| contents | In a previous joint work with Aurichi and Magalhães Jr., we showed that the topological spaces arising from the edge-end structure of infinite graphs define a proper subfamily of those obtained through the well-known (vertex-)ends. This result was later recovered by a more general approach due to Pitz, who also stated the problem of finding a purely topological characterization for the class of edge-end spaces. His question reads as an edge-related version of a similar conjecture posed by Diestel in 1992, but there regarding the usual end structure of infinite graphs and which was recently answered also by Pitz via the existence of a suitable clopen subbase. This paper shows how an extra intersection property can be combined with his solution in order to restrict it to the edge-end spaces, hence stating a topological description for this later family as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A subbase property for describing edge-end spaces Real, Lucas General Topology Combinatorics 05C63, 54F65, 06A07, 54H99 In a previous joint work with Aurichi and Magalhães Jr., we showed that the topological spaces arising from the edge-end structure of infinite graphs define a proper subfamily of those obtained through the well-known (vertex-)ends. This result was later recovered by a more general approach due to Pitz, who also stated the problem of finding a purely topological characterization for the class of edge-end spaces. His question reads as an edge-related version of a similar conjecture posed by Diestel in 1992, but there regarding the usual end structure of infinite graphs and which was recently answered also by Pitz via the existence of a suitable clopen subbase. This paper shows how an extra intersection property can be combined with his solution in order to restrict it to the edge-end spaces, hence stating a topological description for this later family as well. |
| title | A subbase property for describing edge-end spaces |
| topic | General Topology Combinatorics 05C63, 54F65, 06A07, 54H99 |
| url | https://arxiv.org/abs/2508.17424 |