Anchored Hyperspaces and Multigraphs


  • Gerardo Reyna Autonomous University of Guerrero
  • Jesús Romero Autonomous University of Guerrero
  • Ivan Espinobarros Autonomous University of Guerrero



Consider a multigraph $X$ as a metric space and $p \in X$. The anchored hyperspace at $p$ is the set 

$C_p(X) =$ {$A \subseteq X : p \in A, A$ connected and compact}.

In this paper we will prove that $C_p(X)$ is a polytope if in this set is considered the Hausdorff's metric $H$. Further we will show that, if $X$ is a locally connected compact metric space such that $C_p(X)$ is a polytope for each $p \in X$, then $X$ must be a multigraph.

Author Biographies

Gerardo Reyna, Autonomous University of Guerrero

Faculty of Mathematics

Jesús Romero, Autonomous University of Guerrero

Faculty of Mathematics

Ivan Espinobarros, Autonomous University of Guerrero

Faculty of Mathematics


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