Institute of Mathematics AS CR, v. v. i.
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New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators
Get PDFsummary:The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm and a t-conorm by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on , we obtain new classes of uni-nullnorms on via closure (interior) operators. The constructions of uni-nullnorms on some certain classes of bounded lattices can provide another different perspective of t-norms and the dual of t-norms, uninorms and some other associative aggregation operations on bounded lattices. That is, the constructions seem to be the ordinal like sum constructions, but not limited to the ordinal like sum constructions
Additive generators of discrete semi-uninorms
Get PDFsummary:This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in and that are generated by additive generators
The algebraic structure of pseudomeadow
No full textsummary:The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as the subdirect products of fields to the case of commutative pseudomeadows. Finally, we investigate localizations of commutative pseudomeadows
A note on nonseparable Lipschitz-free spaces
No full textsummary:We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property (), Talponen's countable separation property, or being a Gâteaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, the question whether the duals of nonseparable Lipschitz-free spaces have a weak sequentially compact ball is undecidable in ZFC. Finally, we provide an example of a nonseparable dual Lipschitz-free space that fails the Radon--Nikodým property