Ivan Lončar

Arcwise Connected Continua and Whitney Maps

Let $X$ be a non-metric continuum, and $C(X)$ be the hyperspace of subcontinua of $X$. It is known that there is no Whitney map on the hyperspace $2^{X}$ for non-metric Hausdorff compact spaces $X$. On the other hand, there exist non-metric continua which admit and ones which do not admit a Whitney map for $C(X)$. In particular, a locally connected or a rim-metrizable continuum $X$ admits a Whitney map for $C(X)$ if and only if it is metrizable. In this paper we investigate the properties of continua $X$ which admit a Whitney map for $C(X)$ or for $C^{2}(X).$

Arcwise connected continuum, hyperspace, inverse system, property of Kelley, smootness, Whitney map.

MSC 2000: Primary: 54F15, 54B20. Secondary: 54B35