Can an open subset of $\mathbf{R}^m$ be homeomorphic to an open subset of $\mathbf{R}^n$ for $1\leq m<n$?
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
13993
Can we prove $ℝ^n ∖ \{\text{straight line}\}$ and $ℝ^n ∖ \text{\{an axis\}}$ homeomorphic by proving their complements homeomorphic?
143043
When is a local homeomorphism a covering map?
75829
Dimension of open subsets of $R^n$
70264
Prove that the inverse image of an open set is open
56728
Question about limit points of a Subset of $\mathbb{R}$
63701
An example of a regular function over an open set
108687
Open subsets in a manifold as submanifold of the same dimension?
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
73130
A simple question about open set
113915
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
31479
homeomorphism of cantor set extends to the plane?
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
2677
Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?