2012/09/24 by Benjamín Espinoza, Espinoza, Benjamin, Paul Gartside +5
Mathematics · #54F15 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1209.5454
openalex publication_date 2012/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A space is `n-strong arc connected' (n-sac) if for any n points in the space there is an arc in the space visiting them in order. A space is omega-strong arc connected (omega-sac) if it is n-sac for all n. We study these properties in finite graphs, regular continua, and rational continua. There are no 4-sac graphs, but there are 3-sac graphs and graphs which are 2-sac but not 3-sac. For every n there is an n-sac regular continuum, but no regular continuum is omega-sac. There is an omega-sac rational continuum. For graphs we give a simple characterization of those graphs which are 3-sac. It is shown, using ideas from descriptive set theory, that there is no simple characterization of n-sac, or omega-sac, rational continua.