Prove that the complement of an open ball in $\mathbb{R^n}$ has exactly one unbounded component
109046
Is the complement of an open ball in a Banach space connected?
75829
Dimension of open subsets of $R^n$
113696
Showing that the unit ball in $(C^\alpha[a, b], \|\cdot\|_\alpha)$ is compact in $(C[a, b], \|\cdot\|_\infty)$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
36700
Quotient space of closed unit ball and the unit 2-sphere $S^2$
31002
Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact
74996
Extreme point of unit balls, over $\mathbb C$
133884
A proof using Yoneda lemma
69893
An inner product space and its proper closed subspace with trivial orthogonal complement
44912
Prove that $ \overline {A^\complement} = (A°)^\complement $
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
124848
Why $O(n)$ has exactly two connected components?
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
47975
Closed cone in the euclidean space $\mathbb{R}^n$
98756
Unit ball in $C[0,1]$ not sequentially compact
95250
Proof a special extension on the isoperimetric theorem
119003
Complement of $c_{0}$ in $\ell^{\infty}$