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Embeddings of locally connected compacta. (English) Zbl 0604.57012

A map \(f: X\to Y\) of compacta is said to be a cell-like equivalence provided that there exists a compactum Z and cell-like mappings \(g: Z\to X\) and \(h: Z\to Y\) such that \(h=fg\). The author proves that a k- dimensional compactum, which is r-connected and locally r-connected is cell-like equivalent to a compact, k-dimensional, locally r-connected compact subset of \({\mathbb{R}}^{2k-r}\) provided that \(r\leq k-3\). This result is in the direction of Stalling’s theorem, who has proved that k- dimensional, r-connected polyhedra are simple homotopy equivalent to subpolyhedra of \({\mathbb{R}}^{2k-r}\).
Reviewer: J.Grispolakis

MSC:

57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57N60 Cellularity in topological manifolds
57N25 Shapes (aspects of topological manifolds)
54F35 Higher-dimensional local connectedness
57Q35 Embeddings and immersions in PL-topology
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