Shrikhande, Neelima Homotopy properties of decomposition spaces. (English) Zbl 0555.55008 Fundam. Math. 116, 119-124 (1983). 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 Cited in 3 Documents 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 Keywords:nearly 1-movable; shape of a compact connected subspace of Euclidean space; homotopy type of a decomposition space; local simple connectness PDFBibTeX XMLCite \textit{N. Shrikhande}, Fundam. Math. 116, 119--124 (1983; Zbl 0555.55008) Full Text: DOI EuDML