We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...

Monadic MV –algebras are an algebraic model of the predicate calculus of the Lukasiewicz infinite valued logic in which only a single individual variable occurs. GMV -algebras are a non-commutative generalization of MV -algebras and are an algebraic counterpart of the non-commutative Lukasiewicz infinite valued logic. We introduce monadic GMV -algebras and describe their connections to certain ...

We introduce the tense LMn-algebras and the tense MV algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomially equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-algebras) is established. We study the pairs of dually-conjugated operations on MV -algebra...

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...

Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative a...

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical “square” of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and the Malvenuto-Reutenauer Hopf algebra of per...

We present a way to turn an arbitrary (unbounded) metric space $\mathcal{M}$ into bounded $\mathcal{B}$ in such that the corresponding Lipschitz-free spaces $\mathcal{F}(\mathcal{M})$ and $\mathcal{F}(\mathcal{B})$ are isomorphic. The construction we provide is functorial weak sense has advantage of being explicit. Apart from its intrinsic theoretical interest, it many applications allows trans...