In the tree-like representation of time, a relative closeness relation $C$ on the set of histories can be defined by $ C(h,h',h'')\equiv h\cap h'\supset h\cap h''$. We can read $ C(h,h',h'')$ as follows: the history $h$ is closer to $h'$ than to $h''$. In the topological approach, time can be presented as a pair $\langle H, O\rangle$, in which $H$ is a set of histories (viewed as primitive entities) and $O\subseteq \wp H$ is a set of neighborhoods on $H$. Suitable assumptions on $O$ allow us to view this set as the set of moments in a tree. In these structures, $ C(h,h',h'')$ can be defined as follows: $\exists \alpha\in O: h,h´\in \alpha$ and $h''\not\in\alpha$. I will present a further representation of branching-time in which the primitive notions are those of history and of relative closeness relation, so that that time can be viewed as a first-order structure $\langle H, O\rangle$. It will be shown that, in this setting, neighborhoods can be defined and that the conditions under which neighborhoods can be viewed as moments in time, are first-order conditions on $C$.