Show that something is not a sub-manifold
29653
Show that $xy=0$ is a variety but not a manifold
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
132571
Local homeomorphisms which are not covering map?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
73573
image of polynomial map is not an algebraic set
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
61373
A normal subgroup that is not a characteristic
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
113413
How do I show that two groups are not isomorphic?
62950
Use implicit function theorem to show $O(n)$ is a manifold
99755
Non-orientable 1-dimensional (non-hausdorff) manifold
44194
How to show that the unit sphere is a topological manifold?
67383
Prove that $G'$ is not planar.
42714
A diagram which is not the torus
97637
Showing that isotropy groups are submanifolds