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arXiv · 2604.17164

A topological characterization of end space of infinite graphs via games, subspaces and products

Leandro Aurichi·Gustavo Boska·Davide Giacopello·Paulo Magalhães Júnior
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Abstract

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 $G_{\delta}$ subspaces of end spaces are also end spaces, and that the product of end spaces is not always an end space.

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Leandro Aurichi, Gustavo Boska, Davide Giacopello, Paulo Magalhães Júnior. 2026-04-18. A topological characterization of end space of infinite graphs via games, subspaces and products. https://arxiv.org/abs/2604.17164

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