Non-contractible locally connected continua with trivial homotopy groups (Q2219268)

The first author with Eda and Repovš constructed a 2-dimensional simply connected cell-like, yet spherical, Peano continuum [\textit{K. Eda} et al., Mediterr. J. Math. 10, 519--528 (2013; Zbl 1263.54043)]. \textit{U. H. Karimov} and \textit{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.