Point cloud segmentation plays an important role in AI applications such as autonomous driving, AR, and VR. However, previous point cloud segmentation neural networks rarely pay attention to the topological correctness of the segmentation results. In this paper, focusing on the perspective of topology awareness. First, to optimize the distribution of segmented predictions from the perspective of topology, we introduce the persistent homology theory in topology into a 3D point cloud deep learning framework. Second, we propose a topology-aware 3D point cloud segmentation module, TopoSeg. Specifically, we design a topological loss function embedded in TopoSeg module, which imposes topological constraints on the segmentation of 3D point clouds. Experiments show that our proposed TopoSeg module can be easily embedded into the point cloud segmentation network and improve the segmentation performance. In addition, based on the constructed topology loss function, we propose a topology-aware point cloud edge extraction algorithm, which is demonstrated that has strong robustness.