I know a topological space need not be a metric space and every metric space can be considered a topological space (which is the one induced by a metric defined on it).
But, I've come across this question whether it is safe to say that a metric space is 'metrizable'. For ex: The uniform topology(one that is induced by the uniform metric). Does it make sense if the uniform topology is called 'metrizable' since it's a metric space?
I hope someone can clarify this for me.