 Similarly, a countable product of metric spaces can be obtained using the following metric

An uncountable product of metric spaces need not be metrizable.For example, formula_145 is not first-countable and thus isn't metrizable.In the case of a single space formula_1, the distance map formula_147 (from the definition) is uniformly continuous with respect to any of the above product metrics formula_148, and in particular is continuous with respect to the product topology of formula_149.