Another class of distances and continuous quasi-distances in product spaces

We construct a class of continuous quasi-distances in a product of metric spaces and show that,generally,when the parameter (as shown in the paper) is positive,d is a distance and when < 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 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. © 2014 catherine peppo.