On the Topological Properties of Quantized Spaces, I. The Notion of Dimension

An a t t empt is made to define meaningful counterpar ts of topological notions in quantized spaces. Fini tely presented Abelian groups are used as a model for such s p a c e s . Then the notion of dimension is introduced through a recursive definition and it is proven tha t for free Abelian groups it equals the number of generators.