Structural topology optimization seeks to distribute material throughout a design domain in a way that maximizes a certain performance goal. In this work, we solve the topology optimization problem by parameterizing the designs via recently introduced coordinate-based neural networks. Specifically, we show that networks with Fourier feature mapping can achieve state-of-the-art performance. Our method enables the realization of a range of designs using a single mesh via tuning the frequency content of the solutions independently of the finite element discretization grid. This frequency control offers attractive properties, such as mesh-independent results and sub-pixel filtering that leads to appropriate designs for upsampling. We demonstrate our method on the compliance minimization problem, optimizing for the stiffest possible structure within a weight budget for a prescribed set of loads.