Definition 2.1 . [01XV]

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Definition 2.1.

A metric space $Y$ is called $k$ -symmetric if $Y$ is isometric to $\mathds{R}^{k}\times C(Z)$ for some compact metric space $Z$ . We define the closed $k$ th-stratum by

\displaystyle\mathcal{S}^{k}(X)\equiv\{x\in X:\text{ no tangent cone at $x$ is $(k+1)$-symmetric}\}

(2.4)