| Title:
|
Indiscernibles and dimensional compactness (English) |
| Author:
|
Henson, C. Ward |
| Author:
|
Zlatoš, Pavol |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
199-203 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set $u S\subseteq G$ in a biequivalence vector space $\langle W,M,G\rangle$, such that $x - y \notin M$ for distinct $x,y \in u$, contains an infinite independent subset. Consequently, a class $X \subseteq G$ is dimensionally compact iff the $\pi$-equivalence $\doteq_M$ is compact on $X$. This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author. (English) |
| Keyword:
|
alternative set theory |
| Keyword:
|
nonstandard analysis |
| Keyword:
|
biequivalence vector space |
| Keyword:
|
compact |
| Keyword:
|
dimensionally compact |
| Keyword:
|
indiscernibles |
| Keyword:
|
Ramsey theorem |
| MSC:
|
03H05 |
| MSC:
|
46A99 |
| MSC:
|
46S10 |
| MSC:
|
46S20 |
| idZBL:
|
Zbl 0851.46052 |
| idMR:
|
MR1396171 |
| . |
| Date available:
|
2009-01-08T18:23:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118823 |
| . |
| Reference:
|
[{GZ 1985}] Guričan J., Zlatoš P.: Biequivalences and topology in the alternative set theory.Comment. Math. Univ. Carolinae 26.3 525-552. MR 0817825 |
| Reference:
|
[{NPZ 1992}] Náter J., Pulmann P., Zlatoš P.: Dimensional compactness in biequivalence vector spaces.Comment. Math. Univ. Carolinae 33.4 681-688. MR 1240189 |
| Reference:
|
[{ŠZ 1991}] Šmíd M., Zlatoš P.: Biequivalence vector spaces in the alternative set theory.Comment. Math. Univ. Carolinae 32.3 517-544. MR 1159799 |
| Reference:
|
[{SVe 1981}] Sochor A., Vencovská A.: Indiscernibles in the alternative set theory.Comment. Math. Univ. Carolinae 22.4 785-798. MR 0647026 |
| Reference:
|
[{V 1979}] Vopěnka P.: Mathematics in the Alternative Set Theory.Teubner-Verlag Leipzig. MR 0581368 |
| . |
