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Title: Topologies for finite words : compatibility with the cantor topology
Author(s): Staiger, LudwigLook up in the Integrated Authority File of the German National Library
Issue Date: 2024
Type: Article
Language: English
Abstract: Infinite words are often considered as limits of finite words. As topological methods have been proved to be useful in the theory of ω-languages it seems to be providing to include finite and infinite words into one (topological) space. In most cases this results in a poor topological structure induced on the subspace of finite words. In the present paper we investigate the possibility to link topologies in the space of finite words with a topology in the space of infinite words via a natural mapping. A requirement in this linking of topologies consists in the compatibility of the topological properties (openness, closedness etc.) of images with preimages and vice versa. Here, we show that choosing for infinite words the natural topology of the CANTOR space and the δ-limit as linking mapping there are several natural topologies on the space of finite words compatible with the topology of the CANTOR space. It is interesting to observe that besides the well-known prefix topology there are at least two more whose origin is from language theory – centers and supercenters of languages. We show that several of these topologies on the space of finite words fit into a class of ℒ-topologies and exhibit their special properties w.r.t. to the compatibility with the CANTOR topology.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Journal Title: RAIRO / Theoretical informatics and applications
Publisher: EDP Sciences
Publisher Place: Les Ulis
Volume: 58
Issue: 2
Original Publication: 10.1051/ita/2024002
Page Start: 1
Page End: 14
Appears in Collections:Open Access Publikationen der MLU

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