His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. Luneburg's model has been the reference for experimental studies of visual space for almost seventy years. Though theorized to be produced by the brain, the topology of VS is not topologically equivalent (homeomorphic) with the structure and activity of the brain because, as will be shown, the topology of VS cannot be formed from the topology of the brain without tearing and/or cutting and pasting. Applying the method of coordinative definition expounded by Hans Reichenbach for determining geometrical and topological properties of physical space (PS), it can be shown that VS fulfills the topological criteria of being a “real” space sui generis. Instead such properties have been presupposed a priori rather than being established a posteriori by empirical means, perhaps because these properties are self-evident. By contrast the geometrical analysis of VS has taken little cognizance of its topology. Specifically the topological properties of dimensionality, orientability, continuity, and connectivity define “real” space as studied by physics and are the spatial properties that characterize the physical universe as being an integral whole.
For that reason distance is a property not preserved in topological space whereas the property of spatial order is preserved. The empirical study of visual space (VS) has centered on determining its geometry, whether it is a perspective projection, flat or curved, Euclidean or non-Euclidean, whereas the topology of space consists of those properties that remain invariant under stretching but not tearing.
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