Does such a metric space exist that satisfies this property?
2026-04-28 12:23:03.1777378983
Metric space containing distinct points $a$ and $b$ such that $N_R(a) \subset N_r(b)$ where $R > r > 0$
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The discrete metric (all points have distance $1$) works: if $R>r\ge1$ then $N_R(a)$ and $N_r(b)$ are equal to the whole space.