Is an image of a continuous bijection from an open set open in $\mathbb{R}^n$?
4196
A valid proof for the invariance of domain theorem?
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
16654
Unions and Intersections of Open Sets are Open
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
38033
A surjective linear map into a finite dimensional space is open
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
44704
familly of Radially open sets in $\mathbb{R}^2$
91736
Explicit homeomorphism between open and closed rational intervals?
100465
Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
17607
Open maps which are not continuous
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
6491
Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
70264
Prove that the inverse image of an open set is open
46788
Compact open topology on space of continuous maps from a discrete space is a product
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
29154
$f$ is continuous and open implies $f$ injective