query: How we show that $Z := \{(x, y, z) ∈ R^3 | x^2 + y^2 − z^2 = 0\}$ is not a manifold (even it is not a topology manifold)
positive_passages.docid: 151637
positive_passages.text: How do we prove that this set is not manifold?
negative_passages.docid: 73573
negative_passages.text: image of polynomial map is not an algebraic set
negative_passages.docid: 154009
negative_passages.text: Closed, simply connected manifolds which are not spheres
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 84148
negative_passages.text: Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
negative_passages.docid: 29653
negative_passages.text: Show that $xy=0$ is a variety but not a manifold
negative_passages.docid: 98731
negative_passages.text: Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
negative_passages.docid: 135108
negative_passages.text: Why doesn't $ds^2 = 0$ imply two distinct points $p$ and $p'$ on a manifold are the same point?
negative_passages.docid: 73248
negative_passages.text: Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 25854
negative_passages.text: $\mathbb{R}^3$ \ $\mathbb{Q}^3$ is union of disjoint lines. The lines are not in an axis diretion.
negative_passages.docid: 44194
negative_passages.text: How to show that the unit sphere is a topological manifold?
negative_passages.docid: 57310
negative_passages.text: Prove $\mathbb{Z}$ is not a vector space over a field
negative_passages.docid: 24128
negative_passages.text: How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto $R=2(1+\cos \theta)$?
negative_passages.docid: 78873
negative_passages.text: How to show that the monomials are not a Schauder basis for $C[0,1]$
negative_passages.docid: 135241
negative_passages.text: Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group