| Title:
|
Biequivalence vector spaces in the alternative set theory (English) |
| Author:
|
Šmíd, Miroslav |
| Author:
|
Zlatoš, Pavol |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
517-544 |
| . |
| Category:
|
math |
| . |
| Summary:
|
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field $Q$ of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total convexity of the monad and/or of the galaxy of $0$. Finally, the existence of a rather strong type of basis for a fairly extensive area of biequivalence vector spaces, containing all the most important particular cases, is established. (English) |
| Keyword:
|
alternative set theory |
| Keyword:
|
biequivalence |
| Keyword:
|
vector space |
| Keyword:
|
monad |
| Keyword:
|
galaxy |
| Keyword:
|
symmetric Sd-closure |
| Keyword:
|
dual |
| Keyword:
|
valuation |
| Keyword:
|
norm |
| Keyword:
|
convex |
| Keyword:
|
basis |
| MSC:
|
03E70 |
| MSC:
|
03H05 |
| MSC:
|
46A04 |
| MSC:
|
46A06 |
| MSC:
|
46A08 |
| MSC:
|
46A09 |
| MSC:
|
46A35 |
| MSC:
|
46Q05 |
| MSC:
|
46S20 |
| idZBL:
|
Zbl 0756.03027 |
| idMR:
|
MR1159799 |
| . |
| Date available:
|
2009-01-08T17:46:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118431 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
