Prefibers and 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.

THE CATEGORY OF T-CONVERGENCE SPACES AND ITS CARTESIAN-CLOSEDNESS

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

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...

The reliability Wiener number of cartesian product graphs

Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...