Das Produkt von Hüllenstrukturen
Let X denote a locally connected continuum such that cyclic elements have metrizable boundary in X. We study the cyclic elements of X by demonstrating that each such continuum gives rise to an upper semicontinuous decomposition G of X into continua such that X/G is the continuous image of an arc and the cyclic elements of X correspond to the cyclic elements of X/G that are Peano continua.
Let be a Hausdorff space and let be one of the hyperspaces , , or ( a positive integer) with the Vietoris topology. We study the following disconnectedness properties for : extremal disconnectedness, being a -space, -space or weak -space and hereditary disconnectedness. Our main result states: if is Hausdorff and is a closed subset such that (a) both and are totally disconnected, (b) the quotient is hereditarily disconnected, then is hereditarily disconnected. We also...