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Homotopy properties of decomposition spaces. (English) Zbl 0555.55008

The paper establishes that the homotopy type of the decomposition space \(E^ n/X\), where X is a compact connected subset, depends only on the shape of X. Furthermore, since \(E^ n/X\) is locally simply connected if and only if X is nearly 1-movable, the local simple connectness of \(E^ n/X\) also depends only on the shape of X.
Reviewer: J.Walsh

MSC:

55P15 Classification of homotopy type
55P55 Shape theory
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
54B15 Quotient spaces, decompositions in general topology
54C56 Shape theory in general topology
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