The midpoint hyperspace on continua
Abstract
For a metric continuum X , for a Whitney map μ for C ( X ) , and for p ∈ X , we define the midpoint hyperspace M i d μ ( p , X ) as the set containing { p } and all arcs in X whose midpoint is p with respect to μ . We show geometric models of M i d μ ( p , X ) , in the case when X is the arc, the simple closed curve, the simple triod, compactifications of the ray [ 0 , ∞ ) with remainder an arc, compactifications of the real line with remainder an arc, and indecomposable arc continua. Moreover, we present characterizations of dendrites and the arc in terms of this hyperspace.
Fields of Study & Subjects
Advanced Topology and Set Theory
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Topology and its Applications
- Volume
- 383
- Pages
- 109774–109774
- Publication date
- 6 March 2026
- Language
- EN