The structure of classical extensions of quantum probability theory

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed

On some properties of ideal convergent double sequences in fuzzy normed spaces

Recently, Rashid et al. [Rashid, Mohammad HM and Kočinac, Ljubiša DR. Ideal convergence in 2–fuzzy 2–normed spaces, Hacettepe Journal of Mathematics and Statistics, 46(1):149–162, 2017] defined the notion of ideal convergence of single sequences in 2–fuzzy 2–normed linear spaces. The aim of this paper is to generalize this notion to the double sequences in such spaces. For the sake of generalizing we define some concepts that contribute basically to outcomes that we came up with and study some basic properties of these new definitions.Publisher's Versio

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Applications of fuzzy set theory and near vector spaces to functional analysis

We prove an original version of the Hahn-Banach theorem in the fuzzy setting. Convex compact sets occur naturally in set-valued analysis. A question that has not been satisfactorily dealt with in the literature is: What is the relationship between collections of such sets and vector spaces? We thoroughly clarify this situation by making use of R°adstr ¨om’s embedding theorem, leading up to the definition of a near vector space. We then go on to successfully apply these results to provide an original method of proof of Doob’s decomposition of submartingales