Weak forms of G- alph-open sets and decompositions of continuity via grills

Decompositions of Continuity via Ζ−open Sets

Al-Hawary [1] introduced and explored the class of ζ−open sets which is strictly weaker than open and proved that the collection of all ζ−open subsets of a space forms a topology that is finer than the original one. In this paper, we introduce what we call ζ−continuity and ζX−continuity and we give several characterizations and two decompositions of ζ−continuity. Finally, new decompositions of ...

Weak Forms of Continuity and Associated Properties

Properties of Some Weak Forms of Continuity

As weak forms of continuity in topological spaces, weak continuity [I], quasi continuity [2], semi continuity [3] and almost continuity in the sense of Husain [4] are well-known. Recently, the following four weak forms of continuity have been introduced: weak quasi continuity [5], faint continuity [6], subweak continuity [7] and almost weak continuity [8]. These four weak forms of continuity ar...

Sets of Weak Sequential Continuity for Polynomials

Let P : E → K be an N−homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set CP = {x ∈ E : P is weakly sequentially continuous at x}. Introduction Our interest in set of points of weak sequential continuity of a polynomial arises from the following simple observations. If P is any 2−homogeneous scalar valued polynomial on E which is weakly sequentiall...

Decompositions of Some Types of Soft Sets and Soft Continuity via Soft Ideals

In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...