ABSTRACT
A ball U(X) denotes the set of all points in E3 having a distance less than a sufficiently small number eps from the point X. In this case, we measure the distance by the Euclidean norm. A set M C E3 is locally homeomorphic to a subspace En (0 < n < 3) if each ball U(X) C M of any point X G M is homeomorphic to En. Such a set M is called an n-manifold. The manifolds can be classified by their dimensions corresponding to their geometric application to points (n = 0), curves (n = 1), surfaces (n — 2) and solids (n = 3). The n-manifolds are identical to n-dimensional varieties in the topological sense.
