Spaces of Fractional Quotients and Their Properties

Let OX1,…,Xn be a Cartesian coordinate system in the Euclidean space . We partition each Xk-axis with step hk by the points , where is the set of all integer numbers. Then the entire is split into the cells

Here ∏ denotes the Cartesian product of the intervals . In what follows, we use the notation

D(k1,…, kn, h1,…, hn)=D(k, h), k=(k1,…, kn), h=(h1,…, hn).