Distances and continuous quasi-distances in product spaces

【Author】

Catherine Peppo;

【Abstract】

In this article we construct a class of continuous quasidistances in a product of metric spaces,E ,and show that generally,when the parameter λ ( see the main result),is positive d is a distance and when λ < 0,d is only a continuous quasi-distance ,but not a distance .The last conclusion is due to the fact that E is a product space.For the purpose of our main result,we introduce a new definition of density in metric spaces.

【Keywords】

continuous quasi-distance;quasi-metric space;topology

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