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Non-contractible locally connected continua with trivial homotopy groups. (English) Zbl 1458.55010

The first author with Eda and Repovš constructed a 2-dimensional simply connected cell-like, yet spherical, Peano continuum [K. Eda et al., Mediterr. J. Math. 10, 519–528 (2013; Zbl 1263.54043)]. U. H. Karimov and D. Repovš, constructed a non-contractible one-point compactification of a polyhedron with trivial homotopy groups [Proc. Am. Math. Soc. 138, 1525–1531 (2010; Zbl 1196.54057)]. In the present paper, the authors generalize the construction given by Repovš and the first author. They give a cell-like non-contractible \(LC^{\infty}\)-continuum which has trivial homotopy group in each dimension.

MSC:

55Q52 Homotopy groups of special spaces
55N15 Topological \(K\)-theory
54F15 Continua and generalizations
57M05 Fundamental group, presentations, free differential calculus
54G20 Counterexamples in general topology
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