Let <r,θ> be polar coordinates on R².(adsbygoogle = window.adsbygoogle || []).push({});

Define f:R-->R² by f(t)=<e^{t},t>.

Let d_{1}and d_{2}be the metrics on R defined by: d_{1}(t_{1},t_{2}) = |t_{1}- t_{2}|, d_{2}(t_{1},t_{2}) = ||f(t_{1}) - f(t_{2})||

Are d_{1}and d_{2}equivalent? If not, is one finer than the other?

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# Homework Help: Equivalent metrics?

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