**Ivan Lončar**

## Arcwise Connected Continua and Whitney Maps

**Abstract:**

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 $C^{2}(X).$

**Keywords:**

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

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