Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the resolvability of Lindel\"of-generated and (countable
  extent)-generated spaces   Given a topological property $P$, we say that the space $X$ is $P$-generated
if for any subset $A\subset X$ that is not open in $X$ there is a subspace $Y
\subset X$ with property $P$ such that $A\cap Y$ is not open in $Y$. (Of
course, in this definition we could replace "open" with "closed".)
  In this paper we prove the following two results:
  (1) Every Lindel\"of-generated regular space $X$ satisfying
$|X|=\Delta(X)={\omega}_1$ is ${\omega}_1$-resolvable.
  (2) Any (countable extent)-generated regular space $X$ satisfying
$\Delta(X)>{\omega}$ is ${\omega}$-resolvable.
  These are significant strengthenings of our earlier results from [JSSz] which
can be obtained from (1) and (2) by simply omitting the "-generated" part.
Moreover, the second result improves a recent result of Filatova and Osipov
from [FO] which states that Lindel\"of-generated regular spaces of uncountable
dispersion character are 2-resolvable.
  [FO] Maria A. Filatova, Alexander V. Osipov On resolvability of Lindel\"of
generated spaces, arxiv:1712.00803. Siberian Electronic Mathematical Reports,
Vol. 14, (2017) pp. 1444-1444.
  [JSSz] Juh\'asz, Istv\'an; Soukup, Lajos; Szentmikl\'ossy, Zolt\'an, Regular
spaces of small extent are ${\omega}$-resolvable. Fund. Math. 228 (2015), no.
1, 27-46.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat