Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on sets avoiding rational distances   In this paper we shall give a short proof of the result originally obtained
by Ashutosh Kumar that for each $A\subset \mathbb{R}$ there exists $B\subset A$
full in $A$ such that no distance between two distinct points from $B$ is
rational. We will construct a Bernstein subset of $\mathbb{R}$ which also
avoids rational distances. We will show some cases in which the former result
may be extended to subsets of $\mathbb{R}^2$, i. e. it remains true for
measurable subsets of the plane and if $non(\mathcal{N})=cof(\mathcal{N})$ then
for a given set of positive outer measure we may find its full subset which is
a partial bijection and avoids rational distances.

13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph