One-Step Closure, Ideal Convergence and Monotone Determined Space

Lacunary Ideal Convergence in Probabilistic Normed Space

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

Rough ideals based on ideal determined varieties

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

Ideal-determined Categories

We clarify the role of Hofmann’s Axiom in the old-style definition of a semiabelian category. By removing this axiom we obtain the categorical counterpart of the notion of an ideal-determined variety of universal algebras – which we therefore call an ideal-determined category. Using known counter-examples from universal algebra we conclude that there are idealdetermined categories which fail to...

One step forward

Rough Ideal Convergence

In this paper we extend the notion of rough convergence using the concept of ideals which automatically extends the earlier notions of rough convergence and rough statistical convergence. We define the set of rough ideal limit points and prove several results associated with this set.