The unprojectivized Outer space cv_n consists of equivalence classes of all marked metric graph structures on Fn where the volume of the metric graph in the marking is allowed to be any positive real number. The space cv_n can also be thought of as the set of all free minimal discrete isometric actions of Fn on R-trees, considered up to Fn-equivariant isometry. The unprojectivized Outer space inherits the same structures that X_n has, including the coincidence of the three topologies (Gromov, axes, weak), and an \operatorname{Out}(F_n)-action. In addition, there is a natural action of \mathbb R_{>0} on cv_n by scalar multiplication.
