In the enclosed paper, it is
shown that (a) the closed continuous image of a stratifiable space is stratifiable (b)
the well-known extension theorem of Dugundji remains valid for stratifiable spaces
(see Theorem 4.1, Pacific J. Math., 1 (1951), 353–367) (c) stratifiable spaces can be
completely characterized in terms of continuous real-valued functions (d) the
adjunction space of two stratifiable spaces is stratifiable (e) a topological space is
stratifiable if and only if it is dominated by a collection of stratifiable subsets (f) a
stratifiable space is metrizable if and only if it can be mapped to a metrizable space
by a perfect map.
