Náter, J., Pulmann, P., and Zlatoš, Pavol. "Dimensional compactness in biequivalence vector spaces." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 681-688. <http://eudml.org/doc/247371>.
@article{Náter1992,
abstract = {The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a $\pi $-equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set $s$ and classes of set functions $s \rightarrow Q$ is investigated. Finally, a direct connection between compactness of a $\pi $-equivalence $R \subseteq s^2$ and dimensional compactness of the class $\mathbf \{C\}[R]$ of all continuous set functions from $\langle s,R \rangle $ to $\langle Q,\doteq \rangle $ is established.},
author = {Náter, J., Pulmann, P., Zlatoš, Pavol},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {alternative set theory; biequivalence vector space; $\pi $-equivalence; continuous function; set uniform equivalence; compact; dimensionally compact; alternative set theory; set uniform equivalence; dimensionally compact class in a biequivalence vector space; -equivalence; dimensional compactness; Galois connection},
language = {eng},
number = {4},
pages = {681-688},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Dimensional compactness in biequivalence vector spaces},
url = {http://eudml.org/doc/247371},
volume = {33},
year = {1992},
}
TY - JOUR
AU - Náter, J.
AU - Pulmann, P.
AU - Zlatoš, Pavol
TI - Dimensional compactness in biequivalence vector spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 681
EP - 688
AB - The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a $\pi $-equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set $s$ and classes of set functions $s \rightarrow Q$ is investigated. Finally, a direct connection between compactness of a $\pi $-equivalence $R \subseteq s^2$ and dimensional compactness of the class $\mathbf {C}[R]$ of all continuous set functions from $\langle s,R \rangle $ to $\langle Q,\doteq \rangle $ is established.
LA - eng
KW - alternative set theory; biequivalence vector space; $\pi $-equivalence; continuous function; set uniform equivalence; compact; dimensionally compact; alternative set theory; set uniform equivalence; dimensionally compact class in a biequivalence vector space; -equivalence; dimensional compactness; Galois connection
UR - http://eudml.org/doc/247371
ER -
