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arXiv · 2208.07040

A note on sets avoiding rational distances in category bases

Sanjib Basu·Abhit Chandra Pramanik
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Abstract

Michalski gave a short and elegant proof of a theorem of A. Kumar which states that for each set A in R, there exists a subset B of A which is full in A and such that no distance between points in B is a rational number. He also proved a similar theorem for sets in the Euclidean plane. In this paper, we generalize these results in some special types of category bases.

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Sanjib Basu, Abhit Chandra Pramanik. 2022-08-15. A note on sets avoiding rational distances in category bases. https://arxiv.org/abs/2208.07040

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