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### Codimension of the set of topologically singular points of an Alexandrov space.

I am reading Burago, Burago and Ivanov's book A course in metric geometry. In chapter 10 the mention that Alexandrov spaces of curvature bounded below have a stratification into topological manifolds. ...
There is a 50 point bounty on this question. Specifically, I find it appealing to count only squarefree numbers having $k$ prime factors, so I define \pi_k(x)=\#\{n\leq x: ...