Definition talk:Coset Space

I see notation of $G/H^l$ and $G/H^r$ for the first time; I saw that $G/H$ and $G \backslash H$ generalises better with double cosets, especially when notation $G/H$ and $H \backslash G$ is used for left and right coset space respectively (it is less confusing, because as $H$ is subset of $G$ set difference $H \setminus G = \varnothing$ which is in most cases not meaningful in group theory; you might want to reconsider using $S \setminus T$ in favor of $S \smallsetminus T$ which is much more readable). Then double coset space can of $H$ and $K$ in $G$ can be denoted as $H \backslash G / K$. Nonetheless you can mention also about this notation in the article! joel talk 18:23, 29 December 2012 (UTC)