ABSTRACT
This chapter elucidates those somethings that form a primordial physical substrate and determines its mathematical properties. Three new features are introduced to the physical space, namely: structure of space from subquantum to cosmic scales; matter as stable local irregularities of space; space and matter interact and influence each other reciprocally. In a series of works Bounias developed a mathematical theory of space from a canonical particle to the universe. The chapter considers the main determining properties of ordinary space, namely, measure, distances and dimensionality in a broad topological sense. In the case of topological spaces, a space can be subdivided into two main classes - objects and distances. The properties of the set-distance allow the claim that any topological space is metrizable as provided with the set-distance as a natural metric. A mathematical space can give rise to several topologies that range from coarser to finer forms, in an ordered relation.
