Topologie sur l'ensemble des parties positives d'un réseau

Abstract

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 $V^{\ast }$ is the dual vector space of $\RM \otimes_\ZM Λ$.

19 pages. The paper arXiv:0805.3038 has been now divided in two parts: this paper is exactly the sections 2 and 3 of arXiv:0805.3038