The hyperspace of non-cut subcontinua of graphs

2025/03/23 by Illanes, Alejandro, Martínez-de-la-Vega, Verónica, Vega, Jorge E.
#54F50 #54F65 #FOS: Mathematics #General Topology (math.GN) #Primary 54F16 #Secondary 54F15

paper · doi:10.48550/arxiv.2503.18196

Abstract

Given a continuum X, let C(X) be the hyperspace of all subcontinua of X. We consider the hyperspace NC^*(X)=\A∈ C(X):X∖ A is connected\. In this paper we prove that the only locally connected continua X for which NC^*(X) is compact are the arcs and the simple closed curves. We also characterize the finite graphs G for which NC^*(G) is connected.

Related

• Nonblockers for hereditarily decomposable continua with the property of Kelley
• The Hyperspaces C_n(X) of finite ray-graphs
• About the uniqueness of the hyperspaces C(p,X) in some classes of continua
• The hyperspaces HS(p,X)
• The dimension of hyperspaces of non-metrizable continua