Is there non-trivial subset in real line that is both open and closed?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
158569
Proving a particular subset of $R^n$ is closed
152927
seemingly nontrivial question about covering maps and evenly covered open sets
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
23225
Union of connected subsets is connected if intersection is nonempty
5448
Finding the closure of some subsets of the ordered square
72468
Open and closed balls in $C[a,b]$
50846
Is a set without limit points necessarily closed?
137460
How should I think of an open vs. closed set?
15480
Open set in a metric space is union of closed sets
76764
Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
42494
The boundary is a closed set
64861
Intersection of open affines can be covered by open sets distinguished in *both*affines
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
153934
How to prove that a set R\Z is open
99236
Interior of closure of an open set