Another Class of Distances and Continuous Quasi-Distances in Product Spaces

Abstract EN

We construct a class of continuous quasi-distances in a product of metric spaces and show that, generally, when the parameter λ (as shown in the paper) is positive, d is a distance and when λ < 0 , d is only a continuous quasi-distance, but not a distance.

It is remarkable that the same result in relation to the sign of λ was found for two other classes of continuous quasi-distances (see Peppo (2010a, 2010b) and Peppo (2011)).

This conclusion is due to the fact that E is a product space.

For the purposes of our main result, a notion of density in metric spaces is introduced.