We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at $0$. Moreover we show that if two algebraic $(n-1)$-dimensional cones P, R⊂ Cⁿ with isolated singularities are homeomorphic, then they have the same degree.
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Fernandes et al. (2024) studied this question.
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