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In qualitative spatial reasoning, the last ten years have brought a lot of results on theories of spatial properties and relations taking regions of space as primitive entities. In particular, the axiomatization of mereotopologies has been extensively studied. However, properties of space such as divisibility, density and atomicity haven't attracted much attention in this context. Nevertheless, atomicity is especially important if one seeks to build a bridge between spatial reasoning and spatial databases approaches in areas like vision or GIS. In this paper we will investigate the possibility of characterizing such properties in spaces modeled by mereologies and mereotopologies. In addition, properties of atoms like extension and self-connectedness will be considered.

In this paper, we present a theory of space as a framework for spatial reasoning. We believe this formalism is useful for representing geographic space, at least when two constraints are present: a necessity to reason qualitatively over spatial information, and a lack of precise, homogeneous spatial data. This theory is based on mereology, an axiomatic theory of part-whole relation. It includes a formalization of topological concepts as well as some geometric notions, namely distance and orientation. It can be extended to a theory of space-time.