I want to show that $M=\{(x,y,z)\in\mathbb{R}^3|x-y^2=z^2+4,|x|<10\}$ is a submanifold of $\mathbb{R}^3$. The first condition is easy to fulfill with $f(x,y,z):=x-y^2-z^2-4$ and $\{f=0\}$ but how can I treat the second condition?
2026-03-30 07:06:18.1774854378
Proving that set with inequality is a submanifold
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