Abstract:
The space of one-sided infinite words plays a crucial rôle in several
parts of Theoretical Computer Science. Usually, it is convenient to regard
this space as a metric space, the CANTOR space. It turned out that for
several purposes topologies other than the one of the CANTOR space are
useful, e.g. for studying fragments of first-order logic over infinite words
or for a topological characterisation of random infinite words.
It is shown that both of these topologies refine the topology of the CANTOR space. Moreover, from common features of these topologies we extract properties which characterise a large class of topologies. It turns out
that, for this general class of topologies, the corresponding closure and
interior operators respect the shift operations and also, to some respect,
the definability of sets of infinite words by finite automata.