This is an announcement for the paper “A Local Hahn-Banach Theorem and Its Applications” by Niushan Gao<https://arxiv.org/search/math?searchtype=author&query=Gao%2C+N>, Denny H. Leung<https://arxiv.org/search/math?searchtype=author&query=Leung%2C+D+H>, Foivos Xanthos<https://arxiv.org/search/math?searchtype=author&query=Xanthos%2C+F>. Abstract: An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local' version of this theorem. The result is applied to study the uo-dual of a Banach lattice that was recently introduced in [3]. We also provide a simplified approach to the measure-free characterization of uniform integrability established in [8]. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1809.01795