Geodesic
Indiscernibles and dimensional compactness
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 199-203.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 03H05, 46A99, 46S10, 46S20
Keywords: alternative set theory; nonstandard analysis; biequivalence vector space; compact; dimensionally compact; indiscernibles; Ramsey theorem 
@article{CMUC_1996__37_1_a13,
     author = {Henson, C. Ward and Zlato\v{s}, Pavol},
     title = {Indiscernibles and dimensional compactness},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {199--203},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {1996},
     mrnumber = {1396171},
     zbl = {0851.46052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a13/}
}
TY  - JOUR
AU  - Henson, C. Ward
AU  - Zlatoš, Pavol
TI  - Indiscernibles and dimensional compactness
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1996
SP  - 199
EP  - 203
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a13/
LA  - en
ID  - CMUC_1996__37_1_a13
ER  - 
%0 Journal Article
%A Henson, C. Ward
%A Zlatoš, Pavol
%T Indiscernibles and dimensional compactness
%J Commentationes Mathematicae Universitatis Carolinae
%D 1996
%P 199-203
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a13/
%G en
%F CMUC_1996__37_1_a13
Henson, C. Ward; Zlatoš, Pavol. Indiscernibles and dimensional compactness. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 199-203. http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a13/