Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $D$-spaces and Discrete Families of Sets   We prove several reflection theorems on $D$-spaces, which are Hausdorff
topological spaces $X$ in which for every open neighbourhood assignment $U$
there is a closed discrete subspace $D$ such that \[ \bigcup\{U(x): x\in D\}=X.
\] The upwards reflection theorems are obtained in the presence of a forcing
axiom, while most of the downwards reflection results use large cardinal
assumptions.
  The combinatorial content of arguments showing that a given space is a
$D$-space, can be formulated using the concept of discrete families. We note
the connection between non-reflection arguments involving discrete families and
the well known question of the existence of families allowing partial
transversals without having a transversal themselves, and use it to give
non-trivial instances of the incompactness phenomenon in the context of
discretisations.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn