Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Selections of Lower semicontinuous Set-valued Mappings   A space $X$ is strongly $Y$-selective (resp., $Y$-selective) if every lower
semicontinuous mapping from $Y$ to the nonempty subsets (resp., nonempty closed
subsets) of $X$ has a continuous selection. We also call $X$ (strongly)
$C$-selective if it is (strongly) $Y$-selective for any countable space $Y$,
and (strongly) $L$-selective if it is (strongly) ($\omega+1$)-selective. E.
Michael showed that every first countable space is strongly $C$-selective. We
extend this by showing that every $W$-space in the sense of the second author
is strongly $C$-selective. We also show that every GO-space is $C$-selective,
and that every $L$-selective space has Arhangel'skii's property $\alpha_1$. We
obtain an example under $\mathfrak p=\mathfrak c$ of a strongly $L$-selective
space that is not $C$-selective, and we show that it is consistent with and
independent of ZFC that a space is strongly $L$-selective iff it is
$L$-selective and Fr\'echet. Finally, we answer a question of the third author
and Junnila by showing that the ordinal space $\omega_1 +1$ is not
self-selective.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph