How to show that $\partial B(0,1)$ is not weakly closed set?
32555
Prove: The weak closure of the unit sphere is the unit ball.
61316
Sum of closed spaces is not closed
126897
Showing the set $A+B$ is closed.
116806
Find the weak sequential closure of a set in $L^2(-\pi,\pi)$
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
36315
Is $[0,1]$ a countable disjoint union of closed sets?
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 $\mathbb R^1$
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
108740
$C^1[a,b]$ is closed in $C[a,b]$
17461
Show that a set is dense in $[-1,1]$
13906
How to prove the set $S$ is closed under the binary operation $a*b=a+b+kab$?
10180
How to prove that this set is closed?
158155
Is set of isolated points of S closed?
47820
How can I show a supremum of a set is also its limit point?
5251
If $F$ is closed, does there exist a finite measure on $[0,1]$ with support $F$?
53132
A convex subset of a set has 'smaller' boundary than the set?
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?