2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167733We define a notion of {\it positive part} of a lattice $Λ$ 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 $\RM \otimes_\ZM Λ$.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:0805.3038General TopologyGroup Theory06F20 (Primary)text