Image-to-point cloud (I2P) registration is a fundamental task in computer vision, which aims to align pixels in 2D images with corresponding points in 3D point clouds. While deep learning based methods dominate this field, they often fail to generalize to the open domain. In this paper, we address open-domain I2P registration from the topology relationships perspective. Firstly, we find that topology relationships reflect sparse connections between pixels and points, which shows the significant potential in enhancing cross-modality feature interaction in the open domain. Building on this insight, we develop an I2P registration framework using topology relationships. After that, to construct and leverage the topology relationships between the heterogeneous 2D and 3D spaces, we design a registration network, Top-I2P, with correction-based topology reasoning and fast topology feature interaction modules. Extensive experiments on 7-Scenes, RGBD-V2, ScanNet, and self-collected I2P datasets demonstrate that Top-I2P achieves superior registration performance in open-domain scenarios.