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I recently saw this notation being used in the statement of a theorem of De Lellis and Szekelyhidi: The first sentence of the theorem says:

Let $\Omega$ be an open ball in $\mathbb{R}^n$, $T>0$, and $\overline{e}$ a uniformly continuous function $\Omega\times ]O, T[\rightarrow]O, + \infty[$

I have never seen this notation before $]O,T[$, what does it mean when the brackets are outward facing? Any suggested readings would be appreciated. I don't even know what to look up to find this I tried "Outward facing brackets mathematics" but couldn't find anything. Is this notation just really uncommon?

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Reverse brackets indicate open intervals (or if only used at one end of an interval, a semi-open interval).

In many countries it's the only notation used for that, and it's typically less confusing, I'll just refer to the exchange in the comments of another question from earlier today: Why is the set $\mathcal B=\{\,\mathopen]a,b\mathclose[\mid a,b\in\mathbb Q\,\}$ countable?

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    $\begingroup$ “Less confusing” is subjective. It may well be so if you’re used to it. I’m not, so in my mental parser those outward-pointing brackets bind to the arrow instead. $\endgroup$ – amd Aug 25 '18 at 21:43
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Reversed brackets indicate open intevals as $]0,1[$ or semi-open intervals as $[0,1[$, the notation are respectively equivalent to $(0,1)$ and $[0,1)$.

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  • $\begingroup$ Is this notation commonly used? I have never seen it before. $\endgroup$ – Logan Toll Aug 25 '18 at 20:51
  • $\begingroup$ @LoganToll I've already see that in many context. I've added a link form Wiki about that notation. $\endgroup$ – user Aug 25 '18 at 20:52
  • $\begingroup$ @LoganToll It is the standard in France, for instance. $\endgroup$ – Clement C. Aug 25 '18 at 22:23

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