Let $(X,d)$ be a compact [metric space](/page/Metric%20Space), and let $f:X\to X$ be a continuous map. Let $h_{\mathrm{top}}(f)$ denote the Bowen topological entropy of $f$ computed from the Bowen metrics, and let $h_{\mathrm{cov}}(f)$ denote the open-cover topological entropy of $f$. Then