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

Abstract

An attempt is made to define meaningful counterparts of topological notions in quantized spaces. Finitely presented Abelian groups are used as a model for such spaces. Then the notion of dimension is introduced through a recursive definition and it is proven that for free Abelian groups it equals the number of generators. © 1971, ACM. All rights reserved.