On isotopic and discrete realizations of maps of an n-dimensional sphere in Euclidean space

In this paper we consider questions of whether a compact space can be embedded in a Euclidean space. The problem of embedding an 'S-n-like' compact space in R(2n) is solved affirmatively under certain restrictions on the dimension n. We clarify the relations between the realization problem and areas of homotopy theory and differential topology.