Chu spaces from the representational viewpoint

Chu Spaces from the Representational Viewpoint

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.

Chu Spaces

Bifinite Chu Spaces

This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then the existence (or the lack thereof) of the desired colimits. In each case, we provide a characterization of the finite objects in terms of monomorphisms/inj...

Nabla Algebras and Chu Spaces

This paper is a study into some properties and applications of Moss’ coalgebraic or ‘cover’ modality ∇. First we present two axiomatizations of this operator, and we prove these axiomatizations to be sound and complete with respect to basic modal and positive modal logic, respectively. More precisely, we introduce the notions of a modal ∇-algebra and of a positive modal ∇-algebra. We establish ...

Generalizing Topology via Chu Spaces

By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these topological spaces have as special cases known topological spaces. Furthermore, we develop the various topological notions and concepts for GTS. Moreover, since ...