“Social space” constitutes a key idea of Bourdieu’s sociology. According to this concept, social reality in its objectivist aspect can be fundamentally characterized by a multidimensional distribution of agents across social positions. The metatheoretical principle of Bourdieu’s sociology is expressed by the thesis that, by postulating the existence of spatial structure, one can overcome the epistemic difficulties associated with sociological concepts that support a flat ontology within the framework of object-oriented realism. Spatial structure can supply solutions to three major challenges: the first one concerns the tendency for the reification of social order and social phenomena, the second — attributivism, which reduces relationships to characteristics, and the third — the predominance of positivist methodology in sociology. Although Bourdieu claims that spatial structure can be interpreted in terms of a social survey as social space, he goes beyond the boundaries of empirical generalizations. The paper examines the ontology of the idea of “social space”. The authors argue that the postulated spatial structure, which calls for realistic treatment by sociologists, constitutes a metaphysical entity that does not lend itself to complete scientific confirmation. To maintain relative proximity of this metaphysical postulate to scientific practice, Bourdieu identifies the fundamental structure of social reality with topological structure, a concept borrowed from mathematics. Topological structure is perceived as a non-phenomenological law that describes relationships between social positions, interpreted as points in social space. The idea of social space claims the priority of topological structure over social positions, which do not exist before, or separately from, the structure. The article considers three layers in the ontology of “social space”: mathematical, theoretical, and empirical.