The algebra of conditional sets and the concepts of conditional topology and compactness

By Samuel Drapeau, Asgar Jamneshan, Martin Karliczek, Michael Kupper. 2013

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Abstract 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–Smulian theorem are shown.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0b5f220bc8aaa4d93c718163395d9f41959cc8df