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Making holes in the cone, suspension and hyperspaces of some continua

José G. Anaya; Enrique Castañeda-Alvarado; Alejandro Fuentes-Montes de Oca; Fernando Orozco-Zitli — 2018

Commentationes Mathematicae Universitatis Carolinae

A connected topological space $Z$ is unicoherent provided that if $Z = A \cup B$ where $A$ and $B$ are closed connected subsets of $Z$ , then $A \cap B$ is connected. Let $Z$ be a unicoherent space, we say that $z \in Z$ makes a hole in $Z$ if $Z - {z}$ is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.

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