On linking of Cantor sets

We introduce a property L for a subset of a manifold which enables us to pass the geometric linking property from the manifold to this subset. We prove that cubes with handles M and N are linked if and only if subsets X ⊂ Int M and Y ⊂ Int N having property L are linked. We present a criterion which shows that many known Cantor sets explicitly given by defining sequences have this property. As an application of the property L we extend the theorem on rigid Cantor sets thus allowing slightly more complicated terms in their defining sequences