This paper presents a refined transversality theorem using Hausdorff measures, suggesting new applications in singularity theory and generalizing established results.
A transversality theorem is one of the most important tools in singularity theory, and it yields various applications. In this paper, we establish a refined transversality theorem on crossings from a new perspective of Hausdorff measures and give its various applications. Moreover, by using one of them, we generalize Mather's ``stability theorem for generic projections" in his celebrated paper ``Generic projections" under special dimension pairs.
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Shunsuke Ichiki (2025) studied this question.
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