Abstract

We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 Background Chu spaces provide a simple, uniform, and well-structured approach to the representation of objects that may possess algebraic, relational, or other structure, and that can transform into one another in ways that respect that structure. Chu spaces are simple by virtue of being merely a rectangular array, with no further machinery. They are uniform in the sense that all transformable objects, whether sets, groups, Boolean algebras, vector spaces, or manifolds, are representable by Chu spaces within the same framework, and hence can coexist in a single typeless universe of mathematical objects. And they are well-structured in that this seemingly featureless universe in fact has a na...

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