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?
2026-03-27 21:55:47.1774648547
Preservation of compactness under equivalent metrics
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Yes, it is true, since asserting that the metrics are equivalent means that the topologies are the same.