2025/08/24 by Real, Lucas
#05C63 #06A07 #54F65 #54H99 #Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2508.17424
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.