Publikation: The algebra of conditional sets and the concepts of conditional topology and compactness
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2016
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Journal of Mathematical Analysis and Applications. 2016, 437(1), pp. 561-589. ISSN 0002-5232. eISSN 1573-8302. Available under: doi: 10.1016/j.jmaa.2015.11.057
Zusammenfassung
The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional real and functional analysis indicating the possibility of a mathematical discourse based on conditional sets. It is proved that the conditional power set is a complete Boolean algebra, and a conditional version of the axiom of choice, the ultrafilter lemma, Tychonoff's theorem, the Borel–Lebesgue theorem, the Hahn–Banach theorem, the Banach–Alaoglu theorem and the Krein–Šmulian theorem are shown.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Conditional sets; Conditional topology; Conditional compactness; Conditional functional analysis
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DRAPEAU, Samuel, Asgar JAMNESHAN, Martin KARLICZEK, Michael KUPPER, 2016. The algebra of conditional sets and the concepts of conditional topology and compactness. In: Journal of Mathematical Analysis and Applications. 2016, 437(1), pp. 561-589. ISSN 0002-5232. eISSN 1573-8302. Available under: doi: 10.1016/j.jmaa.2015.11.057BibTex
@article{Drapeau2016algeb-29893,
year={2016},
doi={10.1016/j.jmaa.2015.11.057},
title={The algebra of conditional sets and the concepts of conditional topology and compactness},
number={1},
volume={437},
issn={0002-5232},
journal={Journal of Mathematical Analysis and Applications},
pages={561--589},
author={Drapeau, Samuel and Jamneshan, Asgar and Karliczek, Martin and Kupper, Michael}
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