| Informatikai Tanszékcsoport>>> Oktatás>>> | In English |
Topologies for the Set of Disjunctive ω-words
Ludwig Staiger
Abstract:
An infinite sequence (
-word) is referred to as disjunctive provided
it contains every finite word as infix (factor). As
Jürgensen and Thierrin observed the set of
disjunctive -words,
, has a trivial syntactic
monoid but is not accepted by a finite automaton.
In this paper we derive some topological properties of the
set of disjunctive -words. We
introduce two non-standard topologies on the set of all
-words and show that
fulfills some special
properties with respect to these topologies:
In the first topology - the so-called topology of forbidden
words - is the smallest nonempty
-set, and
in the second one is the
set of accumulation points of the whole space as well as
of itself.
Footnotes
... StaigerInstitut für Informatik, Martin-Luther-Universität Halle-Wittenberg, von-Seckendorff-Platz 1, D-06099 Halle, Germany. E-mail: staiger@informatik.uni-halle.de