Semantic segmentation is a fundamental and crucial task that is of great importance to real-world satellite image-based applications. Yet a widely acknowledged issue that occurs when applying the semantic segmentation models to unseen scenery is that the model will perform much poorer than when it was applied to scenery similar to the training data. This phenomenon is usually termed as the domain shift problem. To tackle it, this article presents a self-training-based unsupervised domain adaptation (UDA) method. Different from the previous self-training approaches which focus on rectifying and improving the quality of the pseudo labels, we instead seek to exploit feature-level relation among neighboring pixels to structure and regularize the prediction of the adapted model. Based on the assumption that spatial topological relation is maintained despite the impact of the domain shift, we propose a novel self-training mechanism to perform DA by exploiting local relation in the feature space spanned by the teacher model, from which the pseudo labels are generated. Quantitative experiments on four different public benchmarks demonstrate that the proposed method can outperform the other UDA methods. Besides, analytical experiments also intuitively verify the proposed assumption. Codes will be publicly available at https://github.com/zhu-xlab/PFST .