The Algebra of Conditional Sets and the Concepts of Conditional Topology and Compactness

Authors

Samuel Drapeau, Asgar Jamneshan, Martin Karliczek and Michael Kupper

Date

2016

Journal

Journal of Mathematical Analysis and Applications, 437(1):561-589

Abstract

We introduce the notion of conditional set and conditional inclusion. We show that the resulting conditional power set is a complete Boolean algebra which allows to develop a conditional set theory, topology and functional analysis with a focus on conditional compactness. We construct the conditional real numbers and we prove, among others, the conditional version of the following theorems: Ultrafilter lemma, Tychonoff, Heine-Borel, Banach-Alaoglu and Krein-Šmulian.

Keywords

Conditional Set Theory, Conditional Topology, Conditional Compactness, Conditional Real Numbers, Conditional Duality

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