Some applications of the topological characterizations of the sigma-compact spaces $l\sp{2}\sb{f}$ and $\Sigma$

We use a technique involving skeletoids in $\sigma$-compact metric ARs to obtain some new examples of spaces homeomorphic to the $\sigma$-compact linear spaces $l_f^2$ and $\Sigma$. For example, we show that (1) every ${\aleph_0}$-dimensional metric linear space is homeomorphic to $l_f^2$; (2) every $\sigma$-compact metric linear space which is an AR and which contains an infinite-dimensional compact convex subset is homeomorphic to $\Sigma$; and (3) every weak product of a sequence of $\sigma$-compact metric ARs which contain Hilbert cubes is homeomorphic to $\Sigma$.