Embedding hyperspaces (Q411793)

For a continuum, i.e. a compact connected metric space, with more than one point, the following hyperspaces are considered. \(C(X)\) consists of all subcontinua of \(X\) and \(F_2(X)\) of all nonempty subsets of \(X\) with at most two points. These hyperspaces are endowed with the Hausdorff metric. Classes of continua are studied for which \(F_2(X)\) can be embedded in \(C(X)\). Further locally connected continua \(X\) for which \(C(X)\) can be embedded in some Euclidean space \(\mathbb{R}^n\) are studied.