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I know that there are two different standard notations for a given ball, $B(z, r)$ and $B_r(z)$, but is there a standard notational difference between an open and closed ball?

Paul Frost
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  • I'd write $\overline{B}_r(z)$ for the closed ball and $B_r(z)$ for the open ball. – Joseph Camacho Feb 02 '22 at 19:53
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    It's all not really standard, while $B(x, r)$ usually means open ball, it can mean closed ball as well – Jakobian Feb 02 '22 at 20:37
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    I've seen $U$ used for open and $B$ for closed, $B$ used for open and $\overline{B}$ for closed and $B$ used for open and $D$ for closed. You really just have to confirm whichever convention is being used in whatever text you're reading. – Thorgott Feb 02 '22 at 21:05
  • @JosephCamacho, yes, but see this: https://math.stackexchange.com/questions/108010/when-is-the-closure-of-an-open-ball-equal-to-the-closed-ball – lhf Feb 03 '22 at 10:16
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    "$D$" is quite often used as it stands for "disk". But in general all the symbols mentioned ($B$, $\overline{B}$, $D$, sometimes with indexes $B_r(x)$, sometimes with pairs of arguments $B(x,r)$, etc.) I've seen in papers, so there really is no standard. – freakish Feb 03 '22 at 10:28

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