The main aim of the talk is to propose a new perspective under which branching-time can be investigated. In a tree-like representation of time, the set of histories can be endowed with a topological structure, allowing a topological characterization of basic notions in branching-time semantics. For instance, bundles are dense sets of histories, and a bundle is minimal if and only if the topology induced on it is the discrete topology. Moreover, it will be shown that there is a natural correspondence between non-archimedean topological spaces and bundled trees and that the notions of validity w.r.t. the two kinds of structures coincide.