If J is a set and Xj are topological spaces for each j ∈ J , let X = ∏ j∈J Xj and let πj : X → Xj be the projection maps. A basis for the product topology on X are those sets of the form ⋂ j∈J0 π −1 j (Uj), where J0 is a finite subset of J and Uj is an open subset of Xj , j ∈ J0. Equivalently, the product topology is the initial topology for the projection maps πj : X → Xj , j ∈ J , i.e. the co...

In this paper, we first consider the disjoint union of two fuzzy metric spaces and non-existence of fuzzy contractive maps. We prove that there exists a natural fuzzy metric on the disjoint union of two fuzzy metric spaces. We also show that there is a fuzzy metric space which does not admit any fuzzy contractive map. Second, we introduce the notion of a fuzzy diameter for fuzzy metric spaces a...

The aim of this paper is to extend some fixed point results from [Serban, M. A., Teoria punctului fix pentru operatori definiti pe produs cartezian, Presa Universitar˘a Clujeana Cluj–Napoca, 2002] and [Presic, S. B., Sur une classe d’ inequations aux differences finite et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd) (N. S.). 5(19) (1965), 75-78] in the framework b-metric ...