Abstract
We investigate certain generalized topological structures, with the aim of showing that they can provide a suitable framework within which to compare various approaches to digital topology (including tolerance geometry) with “ordinary” topology. Within an appropriate category of these structures, ordinary spaces arise as inverse limits of digital spaces. In the first instance, the structures can be taken to be (a slight generalization of) C̆ech closure spaces. The structures of this type which seem to be the most useful are those which can be realized as topological graphs (see Section 3). Domain equations for the (real) unit interval provide our main detailed application (Section 4). Another application area which seems promising is that of modal semantics.
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