Arithmetic Operations on Functions from Sets into Functional Sets

Arithmetic Operations on Functions from Sets into Functional Sets

In this paper x, X, X1, X2 are sets. Let Y be a functional set. The functor DOMS(Y ) is defined by: (Def. 1) DOMS(Y ) = ⋃ {dom f : f ranges over elements of Y }. Let us consider X. We say that X is complex-functions-membered if and only if: (Def. 2) If x ∈ X, then x is a complex-valued function. Let us consider X. We say that X is extended-real-functions-membered if and only if: (Def. 3) If x ∈...

On Pre-θ-Open Sets and Two Classes of Functions

Operations on soft sets revisited

Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft sets from given soft sets, some operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true...

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

On the density of integral sets with missing differences from sets related to arithmetic progressions

Article history: Received 23 February 2010 Revised 12 August 2010 Accepted 18 September 2010 Available online xxxx Communicated by Matthias Beck