Topologie sur l'ensemble des parties positives d'un r\'eseau

We define a notion of {\it positive part} of a lattice $\Lambda$ and we endow the set of such positive parts with a topology. We then study some properties of this topology, by comparing it with the one of $V^*/\RM_{> 0}$, where $V^*$ is the dual vector space of $\RM \otimes_\ZM \Lambda$.