Some characterizations of the topological affine spaces are already known [2,5,6]; they are given via the topologies on the sets of points and hyperplanes. According to the definition made by Sorensen in [6], a topological affine space is an affine space whose sets of points and hyperplanes are endowed with non-trivial topologies such that the joining of n independent points, the intersection of n independent hyperplanes and the construction of parallel hyperplanes are continuous operations. In this paper we give a new characterization of such spaces by means of the topologies on the sets of points and lines.