Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological properties of strict $(LF)$-spaces and strong duals of
  Montel strict $(LF)$-spaces   Following [2], a Tychonoff space $X$ is Ascoli if every compact subset of
$C_k(X)$ is equicontinuous. By the classical Ascoli theorem every $k$-space is
Ascoli. We show that a strict $(LF)$-space $E$ is Ascoli iff $E$ is a
Fr\'{e}chet space or $E=\phi$. We prove that the strong dual $E'_\beta$ of a
Montel strict $(LF)$-space $E$ is an Ascoli space iff one of the following
assertions holds: (i) $E$ is a Fr\'{e}chet--Montel space, so $E'_\beta$ is a
sequential non-Fr\'{e}chet--Urysohn space, or (ii) $E=\phi$, so $E'_\beta=
\mathbb{R}^\omega$. Consequently, the space $\mathcal{D}(\Omega)$ of test
functions and the space of distributions $\mathcal{D}'(\Omega)$ are not Ascoli
that strengthens results of Shirai [20] and Dudley [5], respectively.

4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin