In this article, we investigate the descriptive complexity of topological invariants. Our main goal is to understand the expressive power of low complexity invariants, by investigating which spaces they can distinguish. We study the invariants in the first two levels of the Borel hierarchy. We develop techniques to establish whether two spaces can be separated by invariants in these levels. We show that they are sufficient to separate finite topological graphs. We finally identify the complexity of recognizing the line segment.