Resumen:
A connected topological space Z is unicoherent provided that if Z is the union of A and B where A and B are closed connected subsets of Z, then the intersection A and B is connected.
Let Z be a unicoherent space, we say that a point 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.