<p>A core assumption of the conceptual spaces approach is that concepts, which are represented as regions in a space, have prototype structure. This may suggest that the framework cannot be successfully applied to the study of classical concepts based on definitions given by necessary and sufficient conditions. The aim of this paper is to show that this is not the case. By selecting an appropriate space (namely the Cantor space), the framework of conceptual spaces is applied to the study of classical concepts. The points of the space are sets of qualities representing objects, and the topology reflects similarities in respects between these objects. Each classical concept is represented as a region, corresponding to all those objects that share the qualities defining the concept. This model of classical concepts is argued to have several philosophically interesting consequences. First, these regions satisfy plausible adequacy conditions linking similarity and concepts, including Douven-Gärdenfors’s Design Principle of Well-Formedness. Second, these regions are geometrically well-behaved, for they are closed and convex regions with empty boundaries that can also be represented as geometric projections that measure how far an object is from satisfying the definition of the concept. Finally, these regions satisfy a compositionality condition, for they can be combined with each other by combining their definitions. This fact is used to discuss some consequences for the notion of Kantian analyticity as concept containment, in relation to hyperintensional approaches to meaning.</p>