Topologies for the set of disjunctive ω-words

An infinite sequence (ω-word) is referred to as disjunctive provided it contains every finite word as infix (factor). As Jürgensen and Thierrin [JT83] observed the set of disjunctive ω-words, D, has a trivial syntactic monoid but is not accepted by a finite automaton. In this paper we derive some to...

Full description

Saved in:
Bibliographic Details
Main Author: Staiger Ludwig
Format: Article
Published: 2005
Series:Acta cybernetica 17 No. 1
Kulcsszavak:Számítástechnika, Kibernetika
Subjects:
Online Access:http://acta.bibl.u-szeged.hu/12752
Description
Summary:An infinite sequence (ω-word) is referred to as disjunctive provided it contains every finite word as infix (factor). As Jürgensen and Thierrin [JT83] observed the set of disjunctive ω-words, D, 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 ω-words. We introduce two non-standard topologies on the set of all ω-words and show that D fulfills some special properties with respect to these topologies. In the first topology - the so-called topology of forbidden words - D is the smallest nonempty Gδ-set, and in the second one D is the set of accumulation points of the whole space as well as of itself.
Physical Description:43-51
ISSN:0324-721X