2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79496An elementary geometric construction is used to relate the space of lattices in a plane to the space exp_3(S^1) of the subsets of a circle of cardinality at most 3. As a consequence we obtain new proofs of a theorem of Bott which says that exp_3(S^1) is homeomorphic to a 3-sphere and a theorem of Shchepin which says that points of exp_3(S^1) that correspond to one-point subsets form a trefoil knot in this 3-sphere.2 pages, 1 figure; a minor error correctedGeometric TopologyGeneral Topology11H06; 54B20; 57M25text