Geodesic
Making holes in the cone, suspension and hyperspaces of some continua
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 343-364.

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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.
DOI : 10.14712/1213-7243.2015.233
Classification : 54B15, 54B20, 54F55
Keywords: continuum; hyperspace; hyperspace suspension; property (b); unicoherence; cone; suspension 
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     title = {Making holes in the cone, suspension and hyperspaces of some continua},
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Anaya, José G.; Castañeda-Alvarado, Enrique; Oca, Alejandro Fuentes-Montes de; Orozco-Zitli, Fernando. Making holes in the cone, suspension and hyperspaces of some continua. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 3, pp. 343-364. doi : 10.14712/1213-7243.2015.233. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.233/

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