Prove that the set $S=\{f \in C[0,1]|d(f,0)=1\} \subset C[0,1]$ is not compact
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
98756
Unit ball in $C[0,1]$ not sequentially compact
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
102048
Closure of a compact set in Regular space $ X $
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
155063
Is Cl(f(A)) a subset of f(Cl(A))?
146146
Proof that a closed subset of a compact space is a compact space
103125
Show that a non-constant holomorphic function has zeroes in a compact set
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
65180
A compact Hausdorff space that is not metrizable
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
28637
Proving continuous image of compact sets are compact