Vol. 17, No. 1, 1966

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On stratifiable spaces

Carlos Jorge Do Rego Borges

Vol. 17 (1966), No. 1, 1–16

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.

Mathematical Subject Classification
Primary: 54.20
Received: 23 November 1964
Published: 1 April 1966
Carlos Jorge Do Rego Borges