Let $f\colon X\to Y$ be a homeomorphism of finite dimensional Alexandrov spaces with curvature bounded below.
Question: Is it true that for any point $p\in X$ the tangent spaces $T_pX$ and $T_{f(p)}Y$ are homeomorphic with marked points?
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1$\begingroup$ Isn't the tangent cone (assuming tangent space=tangent cone) of an Alexandrov space homeomorphic to a neighborhood of the base point? $\endgroup$Pete– Pete2025-05-12 10:45:08 +00:00Commented May 12 at 10:45
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