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When you construct the largest possible open circle within another open circle, can the radii of both circles be equal to each other? Or does the inner circle need to have a radius strictly < the larger one (when we write the actual inequality)?

Hagen von Eitzen
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mr eyeglasses
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    The two radii are the same if and only if the two centres are the same. Otherwise, the radius of the contained disk is strictly smaller than the radius of the containing disk. – Daniel Fischer Feb 20 '14 at 16:45
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    If by open circle you mean a set of the form $|x|<R$, then the largest open circle contained within an open circle is itself. – copper.hat Feb 20 '14 at 16:45
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    There is no largest open ball properly contained inside another open ball (at least in context of metric spaces). – Marcin Łoś Feb 20 '14 at 16:45
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    In certain metric spaces it is possible that $B(x,r_1)\subseteq B(y,r_2)$ can hold even in some cases where $r_1>r_2$. – Hagen von Eitzen Feb 20 '14 at 17:06

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