Let U be a locally compact Hausdorff space that is not compact. Let L(U) denote the family of continuous real valued functions on U such that for each f ∈ L(U) there is a nonzero number p (depending on f) for which f - p vanishes at infinity. Then L(U) is obviously a lattice under the usual ordering of functions. In this paper we prove that L(U), as a lattice alone, characterizes the locally compact space U. Let S be a locally compact Hausdorff space. Define T(S) to be L(S) if S is not compact, and T(S) to be C(S) if S is compact. We prove that any locally compact Hausdorff spaces S^sub 1^ and S^sub 2^ are homeomorphic if and only if their associated lattices T(S^sub 1^) and T(S^sub 2^) are isomorphic. PUBLICATION ABSTRACT