On the cartesian product of metric spaces

Prefibers and the cartesian product of metric spaces

Tardif, C., Prefibers and the Cartesian product of metric spaces, Discrete Mathematics 109 (1992) 283-288. The properties of certain sets called prefibers in a metric space are used to show that the algebraic properties of the Cartesian product of graphs generalize to metric spaces.

On Set Coverings in Cartesian Product Spaces

The uniform metric on product spaces

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...

On the Structure of Metric-like Spaces

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

Data dependence theorems for operators on cartesian product spaces

We present some abstract data dependence theorems of the fixed point set for operators f, g : X × Y → X × Y , using the c-Picard operators technique. 2000 Mathematical Subject Classification: 47H10.