Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland, e-mail: sliwa@amu.edu.pl
Abstract: We prove that any infinite-dimensional non-archimedean Frechet space $E$ is homeomorphic to $D^{\Bbb N}$ where $D$ is a discrete space with $\card(D)=\dens(E)$. It follows that infinite-dimensional non-archimedean Frechet spaces $E$ and $F$ are homeomorphic if and only if $\dens(E)= \dens(F)$. In particular, any infinite-dimensional non-archimedean Frechet space of countable type over a field $\Bbb K$ is homeomorphic to the non-archimedean Frechet space $\Bbb K^{\Bbb N}$.
Keywords: non-archimedean Frechet spaces, homeomorphisms
Classification (MSC 2000): 46S10
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