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In French, a subset $P \subseteq \mathbb R^n$ that can be written as the product of $n$ finite open intervals is called a "pavé".

Is there a word in English to designate such an object?

quid
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mathcounterexamples.net
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  • I have seen them called open hyperrectangles. – Brian M. Scott Sep 01 '16 at 19:59
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    @WillJagy Does "pavement", "paved thing" or "paving slab" really help the English reader of mathematics in this context? – Patrick Stevens Sep 01 '16 at 20:03
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    @WillJagy then I'd go all the way and use "paver." Or maybe "sett"! We could have a set of setts. :-) – quid Sep 01 '16 at 20:05
  • @PatrickStevens I suppose i don't really know. It helps me when I find a familiar root for a word, so I automatically made a comment. – Will Jagy Sep 01 '16 at 20:48
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    @quid good catch. I know I have seen sett in crossword puzzles, but It is not even in my (early) edition of the OED. https://en.wikipedia.org/wiki/Sett_%28paving%29 – Will Jagy Sep 01 '16 at 20:57
  • @WillJagy to be honest I did not know the word before. What I did know is that while the French word is also used for the pavement, it means the individual stone too and this is the association intended there. So I looked up what that'd be in English. – quid Sep 01 '16 at 21:11
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    @quid this is a link from the wiki page, very nice and more than I knew: http://www.pavingexpert.com/setts01.htm – Will Jagy Sep 01 '16 at 21:13

2 Answers2

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In Rudin's Principles of Mathematical Analysis, the term "$k$-cell" is used for the product of $k$ closed intervals. This appears to be standard enough in English mathematics that it is the title of the relevant Wikipedia article.

Kaj Hansen
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Since a "box" or "brick" is a product of $n$ finite closed intervals, you should be able to use "open box". I would make sure to define it the first time you use it, though, since "open box" is a phrase in colloquial English already.

Patrick Stevens
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