Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $\infty$-convex sets in spaces of scatteredly continuous functions   Given a topological space $X$, we study the structure of $\infty$-convex
subsets in the space $SC_p(X)$ of scatteredly continuous functions on $X$. Our
main result says that for a topological space $X$ with countable strong fan
tightness, each potentially bounded $\infty$-convex subset $F\subset SC_p(X)$
is weakly discontinuous in the sense that each non-empty subset $A\subset X$
contains an open dense subset $U\subset A$ such that each function $f|U$, $f\in
F$, is continuous. This implies that $F$ has network weight $nw(F)\le nw(X)$.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom