Abstract:
We investigate properties of topologies on sets of finite and infinite words over a finite
alphabet. The guiding example is the topology generated by the prefix relation on the
set of finite words, considered as partial order. This partial order extends naturally
to the set of infinite words; hence it generates a topology on the union of the sets
of finite and infinite words. We consider several partial orders which have similar
properties and identify general principles according to which the transition from
finite to infinite words is natural. We provide a uniform topological framework for
the set of finite and infinite words to handle limits in a general fashion.