September 29, 2025Open Access

A note on Automatic Baire property

Key Points

The automatic baire property applies to subsets of the cantor space accepted by finite automata.
It is found that some finite subsets do not fulfill the automatic baire property, indicating gaps in the criteria.
An increase in the computational power of the accepting device may extend beyond the current class of subsets identified.
This work expands the understanding of the relationship between automata theory and topology in mathematical contexts.

Abstract

Automatic Baire property is a variant of the usual Baire property which is fulfilled for subsets of the Cantor space accepted by finite automata. We consider the family A of subsets of the Cantor space having the Automatic Baire property. In particular we show that not all finite subsets have the Automatic Baire property, and that already a slight increase of the computational power of the accepting device may lead beyond the class A.

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Cite This Study

Ludwig Staiger (Sat,) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd11188 https://doi.org/https://doi.org/10.48550/arxiv.2505.18626

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