Staiger Ludwig: Topologies for the set of disjunctive ω-words. In: Acta cybernetica, (17) 1. pp. 43-51. (2005)
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Abstract
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.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Acta cybernetica |
| Date: | 2005 |
| Volume: | 17 |
| Number: | 1 |
| ISSN: | 0324-721X |
| Page Range: | pp. 43-51 |
| Language: | English |
| Place of Publication: | Szeged |
| Related URLs: | http://acta.bibl.u-szeged.hu/38519/ |
| Uncontrolled Keywords: | Számítástechnika, Kibernetika |
| Additional Information: | Bibliogr.: p. 50-51. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.02. Computer and information sciences |
| Date Deposited: | 2016. Oct. 15. 12:25 |
| Last Modified: | 2022. Jun. 15. 12:54 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/12752 |
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