Fell-continuous selections and topologically well-orderable spaces II

Abstract

The present paper improves a result of V. Gutev and T. Nogura (1999) showing that a space $X$ is topologically well-orderable if and only if there exists a selection for $\mathcal{F}_2(X)$ which is continuous with respect to the Fell topology on $\mathcal{F}_2(X)$. In particular, this implies that $\mathcal{F}(X)$ has a Fell-continuous selection if and only if $\mathcal{F}_2(X)$ has a Fell-continuous selection.