Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Collins-Roscoe Structuring Mechanism   A space $X$ has countable $(F)$-property if it has countable point network
satisfying the Collins-Roscoe structuring mechanism. Some sufficient conditions
for $C_p(X)$ having countable $(F)$-property are obtained. As a corollary, we
prove that if $X$ is Corson compact, $C_p(X)$ satisfies countable $(F)$. This
answers a question raised by Tkachuk. Also we get a class of function spaces
with hereditarily $D$-property. We also prove that the countable $(F)$-property
is preserved by taking $\Sigma_s$-product. This answers questions of Tkachuk
positively.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics