Making Holes in the Second Symmetric Product of a Cyclicly Connected Graph

  •  José Anaya    
  •  David Maya    
  •  Fernando Orozco-Zitli    


A \textit{continuum} is a connected compact metric space. The \textit{second symmetric product} of a continuum $ X $, $ \mathcal{F}_2(X) $, is the hyperspace of all nonempty subsets of $ X $ having at most two elements. An element $ A $ of $ \mathcal{F}_2(X) $ is said to \textit{make a hole with respect to multicoherence degree} in $\mathcal{F}_2(X) $ if the multicoherence degree of $ \mathcal{F}_2(X) - \{A\} $ is greater than the multicoherence degree of $ \mathcal{F}_2(X) $. In this paper, we characterize those elements $A \in \mathcal{F}_2(X) $ such that $A$ makes a hole with respect to multicoherence degree in $ \mathcal{F}_2(X) $ when $ X $ is a cyclicly connected graph.

This work is licensed under a Creative Commons Attribution 4.0 License.