Immersions that are not diffeomorphisms from open sets of $\mathbb{R}^n$ to itself
24828
surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
64375
Non-Metrizable Topological Spaces
128266
Dual Spaces and Natural maps
25874
Showing that a certain map is not flat by explicit counterexample
132571
Local homeomorphisms which are not covering map?
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
84707
How to prove a cross is not locally homeomorphic to an euclidean space?
136592
Examples of manifolds that are not boundaries
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
112306
Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic
81546
Prove that function from $S^n \times S^m \to 2S^{m+n+1}$ is immersion
42774
Examples of involutions on $\mathbb{R}$
128410
Showing that the set of fixed points is a smooth manifold
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
80418
The "Easiest" non-smoothable manifold
88981
Explicit Homeomorphism from $\mathbb{R}^2$ to open disk