Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactivorous Sets in Banach Spaces   A set $E$ in a Banach space $X$ is compactivorous if for every compact set
$K$ in $X$ there is a nonempty, (relatively) open subset of $K$ which can be
translated into $E$. In a separable Banach space, this is a sufficient
condition which guarantees the Haar nonnegligibility of Borel subsets. We give
some characterisations of this property in both separable and nonseparable
Banach spaces and prove an extension of the main theorem to countable products
of locally compact Polish groups.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin