Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magic mirrors, dense diameters, Baire category   An old result of Zamfirescu says that for most convex curves $C$ in the plane
most points in $R^2$ lie on infinitely many normals to $C$, where most is meant
in Baire category sense. We strengthen this result by showing that `infinitely
many' can be replaced by `contiunuum many' in the statement. We present further
theorems in the same spirit.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
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The categories of this paper are: stat
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph