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Title: Dimensional compactness in biequivalence vector spaces (English)
Author: Náter, J.
Author: Pulmann, P.
Author: Zlatoš, P.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 33
Issue: 4
Year: 1992
Pages: 681-688
Category: math
Summary: 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 $\bold C[R]$ of all continuous set functions from $\langle s,R \rangle $ to $\langle Q,\doteq \rangle $ is established. (English)
Keyword: alternative set theory
Keyword: biequivalence vector space
Keyword: $\pi$-equivalence
Keyword: continuous function
Keyword: set uniform equivalence
Keyword: compact
Keyword: dimensionally compact
MSC: 03E70
MSC: 03H05
MSC: 46E25
MSC: 46S10
MSC: 46S20
MSC: 46S99
idZBL: Zbl 0784.46064
idMR: MR1240189
Date available: 2009-01-08T17:59:40Z
Last updated: 2012-04-30
Stable URL:
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