  Hippocampal cognitive map---a neuronal representation of the spatial
environment---is broadly discussed in the computational neuroscience literature
for decades. More recent studies point out that hippocampus plays a major role
in producing yet another cognitive framework that incorporates not only
spatial, but also nonspatial memories---the memory space. However, unlike
cognitive maps, memory spaces have been barely studied from a theoretical
perspective. Here we propose an approach for modeling hippocampal memory spaces
as an epiphenomenon of neuronal spiking activity. First, we suggest that the
memory space may be viewed as a finite topological space---a hypothesis that
allows treating both spatial and nonspatial aspects of hippocampal function on
equal footing. We then model the topological properties of the memory space to
demonstrate that this concept naturally incorporates the notion of a cognitive
map. Lastly, we suggest a formal description of the memory consolidation
process and point out a connection between the proposed model of the memory
spaces to the so-called Morris' schemas, which emerge as the most compact
representation of the memory structure.
