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In this paper we define and investigate a new subclass of those Banach spaces which are -analytic in their weak topology; we call them strongly weakly -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not...
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
We define a new large cardinal axiom that fits between and in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".
Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
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