Geodesic
Free spaces
Fundamenta Mathematicae, Tome 163 (2000) no. 3, pp. 229-239 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A space Y is called a free space if for each compactum X the set of maps with hereditarily indecomposable fibers is a dense $G_δ$-subset of C(X,Y), the space of all continuous functions of X to Y. Levin proved that the interval I and the real line ℝ are free. Krasinkiewicz independently proved that each n-dimensional manifold M (n ≥ 1) is free and the product of any space with a free space is free. He also raised a number of questions about the extent of the class of free spaces. In this paper we will answer most of those questions. We prove that each cone is free. We introduce the notion of a locally free space and prove that a locally free ANR is free. It follows that every polyhedron is free. Hence, 1-dimensional Peano continua, Menger manifolds and many hereditarily unicoherent continua are free. We also give examples that show some limits to the extent of the class of free spaces.
DOI : 10.4064/fm-163-3-229-239
Keywords: free space, hereditarily indecomposable continuum, polyhedron

Jianwei Song 1 ; E. D. Tymchatyn 1

1 
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Jianwei Song; E. D. Tymchatyn. Free spaces. Fundamenta Mathematicae, Tome 163 (2000) no. 3, pp. 229-239. doi: 10.4064/fm-163-3-229-239

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