  Let $G$ be a complex affine algebraic group and $H, F \subset G$ be closed
subgroups. The homogeneous space $G / H$ can be equipped with structure of a
smooth quasiprojective variety. The situation is different for double coset
varieties $\dcosets{F}{G}{H}$. In this paper we give examples showing that the
variety $\dcosets{F}{G}{H}$ does not necessarily exist. We also address the
question of existence of $\dcosets{F}{G}{H}$ in the category of constructible
spaces and show that under sufficiently general assumptions $\dcosets{F}{G}{H}$
does exist as a constructible space.
