English

A note on sets avoiding rational distances in category bases

Functional Analysis 2022-08-16 v1

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.

Keywords

Cite

@article{arxiv.2208.07040,
  title  = {A note on sets avoiding rational distances in category bases},
  author = {Sanjib Basu and Abhit Chandra Pramanik},
  journal= {arXiv preprint arXiv:2208.07040},
  year   = {2022}
}
R2 v1 2026-06-25T01:42:24.253Z