Experience is a process of awareness and mastery of facts or events, gained through actual observation or second-hand knowledge. Recent findings reinforce the idea that a naturalized epistemological approach is needed to further advance our understanding of the nervous mechanisms underlying experience. This essay is an effort to build a coherent topological-based framework able to elucidate particular aspects of experience, e.g., how it is acquired by a single individual, transmitted to others and collectively stored in form of general ideas. Taking into account concepts from neuroscience, algebraic topology and Richard Avenarius’ philosophical analytical approach, we provide a scheme which is cast in an empirically testable fashion. In particular, we emphasize the foremost role of variants of the Borsuk-Ulam theorem, which tells us that, when a pair of opposite (antipodal) points on a sphere are mapped onto a single point in Euclidean space, the projection provides a description of both antipodal points. These antipodes stand for nervous functions and activities of the brain correlated with the mechanisms of acquisition and transmission of experience.