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...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

Sometimes we have to work with  $L$-fuzzy context sequences where one or more values are missing. These sequences can represent, among other things, the evolution in time of an $L$-fuzzy context. The studies of tendencies that we have done so far used tools that are not valid when the $L$-fuzzy context has unknown values. In this work we address such situations and we propose new methods to tac...

Amonge other things we give sufficient and necessary conditions for the Lau product of Banachalgebras to be biflat or biprojective.

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.

Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.

the islamic civilization in its prosperous and dynamic period has had various social and economic institutions, an outstanding example of which has been the textile industry. a considerable part of this industry has been active under the name of ṭirāz and the related organization, influencing on most aspects of the muslims’ life. besides their major economic impacts on islamic community, ṭirāz ...

in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...