| Title:
|
On topological classification of non-archimedean Fréchet spaces (English) |
| Author:
|
Śliwa, Wiesław |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
457-463 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\mathbb{K}^{\mathbb{N}}$. (English) |
| Keyword:
|
non-archimedean Fréchet spaces |
| Keyword:
|
homeomorphisms |
| MSC:
|
46A04 |
| MSC:
|
46S10 |
| idZBL:
|
Zbl 1080.46525 |
| idMR:
|
MR2059266 |
| . |
| Date available:
|
2009-09-24T11:14:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127903 |
| . |
| Reference:
|
[1] L. E. J. Brouver: On the structure of perfect sets of points.Proc. Acad. Amsterdam 12 (1910), 785–794. |
| Reference:
|
[2] J. Kąkol, C. Perez-Garcia and W. Schikhof: Cardinality and Mackey topologies of non-Archimedean Banach and Fréchet spaces.Bull. Polish Acad. Sci. Math. 44 (1996), 131–141. MR 1416418 |
| Reference:
|
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| Reference:
|
[4] A. C. M. van Rooij: Notes on $p$-adic Banach spaces.Report 7633, Mathematisch Instituut, Katholieke Universiteit, Nijmegen, The Netherlands, 1976, pp. 1–62. |
| Reference:
|
[5] A C. M. van Rooij: Non-Archimedean Functional Analysis.Marcel Dekker, New York, 1978. Zbl 0396.46061, MR 0512894 |
| Reference:
|
[6] W. H. Schikhof: Locally convex spaces over non-spherically complete valued fields.Bull. Soc. Math. Belgique 38 (1986), 187–207. MR 0871313 |
| Reference:
|
[7] W. Śliwa: Examples of non-archimedean nuclear Fréchet spaces without a Schauder basis.Indag. Math. (N.S.) 11 (2000), 607–616. MR 1909824, 10.1016/S0019-3577(00)80029-4 |
| . |
