Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measure of compactness for filters in product spaces:
  Kuratowski-Mr\`owka in CAP revisited   The first author introduced a measure of compactness for families of sets,
relative to a class of filters, in the context of convergence approach spaces.
We characterize a variety of maps (types of quotient maps, closed maps, and
variants of perfect maps) as those respecting this measure of compactness under
one form or another. We establish a product theorem for measure of compactness
that yields as instances new product theorems for spaces and maps, and new
product characterizations of spaces and maps, thus extending existing results
from the category of convergence spaces to that of convergence approach spaces.
In particular, results of the Mr\`owka-Kuratowski type are obtained, shedding
new light on existing results for approach spaces.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin