On topological classification of non-archimedean Fréchet spaces
Czechoslovak Mathematical Journal (2004)
- Volume: 54, Issue: 2, page 457-463
- ISSN: 0011-4642
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topŚliwa, Wiesƚaw. "On topological classification of non-archimedean Fréchet spaces." Czechoslovak Mathematical Journal 54.2 (2004): 457-463. <http://eudml.org/doc/30875>.
@article{Śliwa2004,
abstract = {We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^\{\mathbb \{N\}\}$ where $D$ is a discrete space with $\mathop \{\mathrm \{c\}ard\}(D)=\mathop \{\mathrm \{d\}ens\}(E)$. It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $\mathop \{\mathrm \{d\}ens\}(E)= \mathop \{\mathrm \{d\}ens\}(F)$. 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 $\mathbb \{K\}^\{\mathbb \{N\}\}$.},
author = {Śliwa, Wiesƚaw},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-archimedean Fréchet spaces; homeomorphisms; non-archimedean Fréchet spaces; homeomorphisms},
language = {eng},
number = {2},
pages = {457-463},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On topological classification of non-archimedean Fréchet spaces},
url = {http://eudml.org/doc/30875},
volume = {54},
year = {2004},
}
TY - JOUR
AU - Śliwa, Wiesƚaw
TI - On topological classification of non-archimedean Fréchet spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 457
EP - 463
AB - We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^{\mathbb {N}}$ where $D$ is a discrete space with $\mathop {\mathrm {c}ard}(D)=\mathop {\mathrm {d}ens}(E)$. It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $\mathop {\mathrm {d}ens}(E)= \mathop {\mathrm {d}ens}(F)$. 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 $\mathbb {K}^{\mathbb {N}}$.
LA - eng
KW - non-archimedean Fréchet spaces; homeomorphisms; non-archimedean Fréchet spaces; homeomorphisms
UR - http://eudml.org/doc/30875
ER -
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