Subword topology

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Abstract

We introduce a topology on a language LX, called subword topology, which reflects certain interesting properties of subwords in a language. Well-known topological concepts such as compactness, closure of a language and closed sets reflect certain characteristic properties of subwords. The concept of adherence of a language (Nivat, 1979) is generalized to that of subword adherence and comparison is made with other limiting processes. The study of closed sets throws further light on Ehrenfeucht's Conjecture (Choffrut and Culik II, 1984) on unavoidable sets and generalizes it.

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