ON UNICOHERENCE AND CONTRACTIBILITY OF HYPERSPACES OF NONMETRIZABLE CONTINUA

Let X be a Hausdorff continuum (a nondegenerate, compact, connected Hausdorff space). Let C(X) denote the hyperspace of its subcontinua, endowed with the Vietoris topology. We extend some results of the metric case about unicoherence and the existence of selections for C(X). We also introduce two definitions of contractibility of C(X) and discuss their relation with some properties of X. In particular, we show that both definitions are equivalent in the metrizable case, but one of them is more general in the Hausdorff continuum case.