On noncontractible compacta with trivial homology and homotopy groups

Umed H. Karimov, Dušan Repovš

We construct an example of a Peano continuum $X$ such that: (i) $X$ is a one-point compactification of a polyhedron; (ii) $X$ is weakly homotopy equivalent to a point (i.e. $π_n(X)…