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- W2604076233 abstract "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 Frechet 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 Frechet--Montel space, so $E'_beta$ is a sequential non-Frechet--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." @default.
- W2604076233 created "2017-04-07" @default.
- W2604076233 creator A5023391268 @default.
- W2604076233 date "2017-02-25" @default.
- W2604076233 modified "2023-09-27" @default.
- W2604076233 title "Topological properties of strict $(LF)$-spaces and strong duals of Montel strict $(LF)$-spaces" @default.
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