Many wireless vision applications, such as autonomous driving, require preservation of global structural information rather than only per-pixel fidelity. However, existing Deep joint source-channel coding (DeepJSCC) schemes mainly optimize pixel-wise losses and provide no explicit protection of connectivity or topology. This letter proposes TopoJSCC, a topology-aware DeepJSCC framework that integrates persistent-homology regularizers to end-to-end training. Specifically, we enforce topological consistency by penalizing Wasserstein distances between cubical persistence diagrams of original and reconstructed images, and between Vietoris--Rips persistence of latent features before and after the channel to promote a robust latent manifold. TopoJSCC is based on end-to-end learning and requires no side information. Experiments show improved topology preservation and peak signal-to-noise ratio (PSNR) in low signal-to-noise ratio (SNR) and bandwidth-ratio regimes.