Are the only sets in $\mathbb{R^1}$ which are both open and closed $\mathbb{R^1}$ and $\emptyset$?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
5022
Can a set containing $0$ be purely imaginary?
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
28683
Sum of two closed sets in $\mathbb R$ is closed?
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
94825
Open set as a finite union of closed sets
72468
Open and closed balls in $C[a,b]$
79424
Don't understand proof that interior of a set is open
1307
Infimum and supremum of the empty set
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
42494
The boundary is a closed set
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
78399
In $T_1$ space, all singleton sets are closed?
50344
What is the closure of an open ball $B_X(\mathbf{a},r)$ in $X=\mathbb{R}^n$?