It has been shown that every Borel subset of density topology X is d-$G_delta$. I’m curious about its connection to the euclidean topology. For example, is the close/open set in the density topology a $G_delta$ set in Euclidean topology? It seems false to me; for example, pick a non-Borel set S of Lebesgue measure 0, then it’s closed in the density topology but definitely not a $G_delta$ set in Euclidean topology. But I would like to know more about the connections between sets in density topology and its euclidean counterpart. Is there any related theorem on this subject?