A Compactification of Polynomial Coalgebras
Coalgebras of polynomial functors on the category of sets have proven
useful in
theoretical computer science for modelling various types of data
structures and
state-transition systems. These coalgebras are shown to have an
intrinsic
topology with respect to which all coalgebraic morphisms are continuous.
The main purpose of the paper is to describe a certain ``Stone space
like''
construction of the \textit{definable enlargement} of a coalgebra, and
show that
it has a topological characterization reminiscent of the Stone-\v{C}ech
compactification.