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 |