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

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