Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new Cartan-type property and strict quasicoverings when $p=1$ in
  metric spaces   In a complete metric space that is equipped with a doubling measure and
supports a Poincar\'e inequality, we prove a new Cartan-type property for the
fine topology in the case $p=1$. Then we use this property to prove the
existence of $1$-finely open \emph{strict subsets} and \emph{strict
quasicoverings} of $1$-finely open sets. As an application, we study fine
Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined
on $1$-finely open sets.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom