%0 Journal Article %T Topologies on the set of all subspaces of a banach space and related questions of banach space geometry %A Mikhail I. Ostrovskii %J Mathematics %D 1993 %I arXiv %X For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two the most common topologies on $G(X)$. %U http://arxiv.org/abs/math/9303202v1