# Preservation of compactness under equivalent metrics

Let $$X$$ be a compact metric space under a certain metric $$d_1$$.

Let $$d_2$$ be a metric equivalent to $$d_1$$. Is it true that $$(X,d_2)$$ is a compact metric space?

If so how do I go about proving it?

• Compactness is a property of the topology. Equivalent metrics generate the same topology. – DanielWainfleet Apr 18 '18 at 5:27