Topologies for the set of disjunctive ω-words

Staiger, Ludwig: Topologies for the set of disjunctive ω-words. In: Acta cybernetica, (17) 1. pp. 43-51. (2005)

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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: angol
Uncontrolled Keywords: Természettudomány
Additional Information: Bibliogr.: p. 50-51.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Jun. 05. 13:46

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