Is there a name for sets in $\mathbb{R}^d$ of the form $$ (-\infty,r_1]\times(-\infty,r_2]\times\cdots\times(-\infty,r_d], $$ where $r_1,\ldots,r_d$ are real numbers?
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1Half-open $d$-dimensional unbounded rectangles? https://proofwiki.org/wiki/Definition:Half-Open_Rectangle except usually the half-open end is the upper end of each interval. Possibly "generalised quadrant" although in 3 dimensions it's an octant. – Prime Mover May 07 '21 at 20:13
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Product of half-infinite closed intervals? – kimchi lover May 07 '21 at 20:33
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A translated (shifted) orthant. – RobertTheTutor May 08 '21 at 00:53