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.
@article{118823,
author = {C. Ward Henson and Pavol Zlato\v s},
title = {Indiscernibles and dimensional compactness},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {199-203},
zbl = {0851.46052},
mrnumber = {1396171},
language = {en},
url = {http://dml.mathdoc.fr/item/118823}
}
Henson, C. Ward; Zlatoš, Pavol. Indiscernibles and dimensional compactness. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 199-203. http://gdmltest.u-ga.fr/item/118823/
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