# Indiscernibles and dimensional compactness

Commentationes Mathematicae Universitatis Carolinae (1996)

- Volume: 37, Issue: 1, page 199-203
- ISSN: 0010-2628

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topHenson, C. Ward, and Zlatoš, Pavol. "Indiscernibles and dimensional compactness." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 199-203. <http://eudml.org/doc/247915>.

@article{Henson1996,

abstract = {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.},

author = {Henson, C. Ward, Zlatoš, Pavol},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem; nonstandard analysis; dimensionally compact; indiscernibles; Ramsey theorem; alternative set theory; biequivalence vector space},

language = {eng},

number = {1},

pages = {199-203},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Indiscernibles and dimensional compactness},

url = {http://eudml.org/doc/247915},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Henson, C. Ward

AU - Zlatoš, Pavol

TI - Indiscernibles and dimensional compactness

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1996

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 37

IS - 1

SP - 199

EP - 203

AB - 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.

LA - eng

KW - alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem; nonstandard analysis; dimensionally compact; indiscernibles; Ramsey theorem; alternative set theory; biequivalence vector space

UR - http://eudml.org/doc/247915

ER -

## References

top- Guričan J., Zlatoš P., Biequivalences and topology in the alternative set theory, Comment. Math. Univ. Carolinae 26.3 525-552. MR0817825
- Náter J., Pulmann P., Zlatoš P., Dimensional compactness in biequivalence vector spaces, Comment. Math. Univ. Carolinae 33.4 681-688. MR1240189
- Šmíd M., Zlatoš P., Biequivalence vector spaces in the alternative set theory, Comment. Math. Univ. Carolinae 32.3 517-544. MR1159799
- Sochor A., Vencovská A., Indiscernibles in the alternative set theory, Comment. Math. Univ. Carolinae 22.4 785-798. MR0647026
- Vopěnka P., Mathematics in the Alternative Set Theory, Teubner-Verlag Leipzig. MR0581368

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