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Keywords:
continuum; hyperspace; hyperspace suspension; property (b); unicoherence; cone; suspension
continuum; hyperspace; hyperspace suspension; property (b); unicoherence; cone; suspension
Summary:
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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