A subbase property for describing edge-end spaces

Lucas Real

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arXiv · 2508.17424

A subbase property for describing edge-end spaces

Lucas Real

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Abstract

In a previous joint work with Aurichi and Magalh\~aes 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.

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Lucas Real. 2025-08-24. A subbase property for describing edge-end spaces. https://arxiv.org/abs/2508.17424

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