José G. Anaya, Enrique Castañeda-Alvarado, Alejandro Fuentes-Montes de Oca, Fernando Orozco-Zitli
Making holes in the cone, suspension and hyperspaces of some continua

Comment.Math.Univ.Carolin. 59,3 (2018) 343-364.

Abstract:A connected topological space $Z$ is {\it 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.

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

DOI: DOI 10.14712/1213-7243.2015.233
AMS Subject Classification: 54B15 54B20 54F55