In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

The uniform box product was introduced by Scott Williams in 2001, but very little was done with it until the recent (2010 and 2012) [B1], [H1] dissertations of Jocelyn Bell and Jeffrey Hankins. Their results had to do with two questions that Williams posed a decade earlier: whether the uniform box product of compact spaces is normal, and whether it is paracompact. Hankins answered the latter qu...

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. 4. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions. In...

whenever ‖~v‖V < δ. In this case the bounded linear operator dF~v0 is called the (Frechet) derivative of F at ~v0. Prove that if ‖ • ‖V is a norm on V which is equivalent to ‖ • ‖V , then F is differentiable at ~v9 with respect to ‖ • ‖V if and only if it is differentiable at ~v0 with respect to ‖ • ‖V , and in this case the derivatives are equal. Similarly, if ‖ • ‖W is a norm on W which is eq...

We give a complete characterisation of the sets in which Peano derivatives of functions, which are definable in an o-minimal expansion of a real closed field, are continuously respectively Fréchet differentiable.

Some aspects of the theory of Boolean algebras and distributive lattices -in particular, the Stone Representation Theorems and the properties of filters and ideals -are analyzed in a constructive setting.

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

Let X = lp, p ∈ (2,+∞). We construct a function f : X → R which has Lipschitz Fréchet derivative on X but is not a d.c. function.