Is unit ball in $L_2(0,1)$ closed in $L_1(0,1)$?
117508
Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$
86717
Completeness of $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle$
78399
In $T_1$ space, all singleton sets are closed?
111830
When is the closure of an open ball equal to the closed ball?
156101
Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
98756
Unit ball in $C[0,1]$ not sequentially compact
118272
Show that $L^1$ is strictly contained in $(L^\infty)^*$
92774
Prove that a linear subspace of $C([0,1])$ is closed
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
149971
Closed unit disk homeomorphic to $\mathbb{R}^2$?
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
32555
Prove: The weak closure of the unit sphere is the unit ball.
143457
Is product of two closed sets closed?
99675
A closed ball in $l^{\infty}$ is not compact
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence
52014
Showing $(C[0,1], d_1)$ is not a complete metric space