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A note on Kieboom’s pullback theorem for cofibrations. (English) Zbl 1154.55006

From the abstract: The aim of this paper is to show that Kieboom’s Pullback Theorem for Cofibrations [R. W. Kieboom, Arch. Math. 45, 68–73 (1985; Zbl 0604.55007)] has many important applications and gives generalizations of some well known classical results of homotopy theory. Kieboom has shown that Strøm’s Pullback Theorem (Theorem 12 in [A. Strøm, Math. Scand. 22, 130–142 (1968; Zbl 0181.26504)]) is a special case of his theorem and has given a number of applications of his theorem on locally equiconnected spaces. In this paper, the author presents more important applications of Kieboom’s theorem and shows that a version of the main theorem of his paper [R.W. Kieboom, Bull. Soc. Math. Belg., Sér. B 39, 203–207 (1987; Zbl 0645.55005)] is in fact a consequence of his Pullback Theorem thereby demonstrating that most of the well known classical results of Strøm are in fact special cases of the Pullback Theorem.

MSC:

55P05 Homotopy extension properties, cofibrations in algebraic topology
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References:

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