How to show explicitly that $\{(x, y)| x^3 = y^2\}$ is not a smooth manifold?
95221
Is the cuspidal cubic $\{y^2 = x^3\} \subset \Bbb R^2$ not smooth?
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
96303
When does $h(x^2+y^2)$ be harmonic?
29653
Show that $xy=0$ is a variety but not a manifold
144548
topological structure on smooth manifolds
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
79727
Direct proof of non-flatness
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
116659
Manifold that is NOT smooth
9793
Why is the image of a smooth embedding $f: N \to M$ an embedded submanifold?
78085
A non orientable closed surface cannot be embedded into $\mathbb{R}^3$
40293
Understanding the definition of norm of tensors on a Riemannian manifold
109027
example of a non differentiable manifold
90092
Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
152725
Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
154496
Proving that the Hopf map $S^3 \to S^2$ is a submersion
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?