  A generalization of the triangle inequality is introduced by a mapping
similar to a t-conorm mapping. This generalization leads us to a notion for
which we use the $\star$-metric terminology. We are interested in the
topological space induced by a $\star$-metric. Considering some examples of
non-trivial $\star$-metrizable topological spaces, we also study the product
topology for a finite family of $\star$-metrizable topological spaces.
