On topological classification of non-archimedean Fréchet spaces
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 457-463
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^{\mathbb{N}}$ where $D$ is a discrete space with $\mathop {\mathrm card}(D)=\mathop {\mathrm dens}(E)$. It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $\mathop {\mathrm dens}(E)= \mathop {\mathrm dens}(F)$. In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field $\mathbb{K}$ is homeomorphic to the non-archimedean Fréchet space $\mathbb{K}^{\mathbb{N}}$.
We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^{\mathbb{N}}$ where $D$ is a discrete space with $\mathop {\mathrm card}(D)=\mathop {\mathrm dens}(E)$. It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $\mathop {\mathrm dens}(E)= \mathop {\mathrm dens}(F)$. In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field $\mathbb{K}$ is homeomorphic to the non-archimedean Fréchet space $\mathbb{K}^{\mathbb{N}}$.
@article{CMJ_2004_54_2_a17,
author = {\'Sliwa, Wies{\l}aw},
title = {On topological classification of non-archimedean {Fr\'echet} spaces},
journal = {Czechoslovak Mathematical Journal},
pages = {457--463},
year = {2004},
volume = {54},
number = {2},
mrnumber = {2059266},
zbl = {1080.46525},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a17/}
}
Śliwa, Wiesław. On topological classification of non-archimedean Fréchet spaces. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 457-463. http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a17/