On linking of cycles in locally connected spaces

The paper is devoted to studying the linking of cycles with compacta in LCn-spaces and in particular homology Z-sets. The main two consequences of our considerations are the following: is proved that a k-dimensional polyhedron cannot link a (n−k−1)-dimensional cycle in an n-dimensional Menger manifold. is proved that a compact set in an ENR is a homology Z-set provided all its points are homology Z-sets.