 The topology on affinoids is subtle, using notions of "affinoid subdomains" (which satisfy a universality property with respect to maps of affinoid algebras) and "admissible open sets" (which satisfy a finiteness condition for covers by affinoid subdomains).In fact, the admissible opens in an affinoid do not in general endow it with the structure of a topological space, but they do form a Grothendieck topology (called the "G"-topology), and this allows one to define good notions of sheaves and gluing of spaces.A rigid analytic space over "k" is a pair formula_3 describing a locally ringed "G"-topologized space with a sheaf of "k"-algebras, such that there is a covering by open subspaces isomorphic to affinoids.