Prove that:
$$Z:=\left\{(x,y,z) \in \mathbb{R}^3\mid x^2 +y^2-z^2=0\right\}$$
is not a manifold (even not a topological manifold).
2026-04-01 10:03:21.1775037801
How do we prove that the double cone is not manifold?
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$Z\setminus\{(0,0,0)\}$ is not connected - that can only happen with 1-dimensional manifolds. But a neighbourhood of e.g. $(1,0,1)$ clearly looks 2-dimensionsl.