We consider the problem of choosing a set of locations of a public good on the real line R when agents have single-peaked preferences over points. We ordinally extend preferences over compact subsets of R, and extend the results of Ching and Thomson (1996), Vohra (1999), and Klaus (2001) to choice correspondences. We show that efficiency and replacement-dominance characterize the class of target point functions (Corollary 2) while efficiency and population-monotonicity characterize the class of target set correspondences (Theorem 1).