Proving $K$ is compact directly.
19111
If every real-valued continuous function is bounded on $X$ (metric space), then $X$ is compact.
1756
1-point compactification and embedding
50266
In the following figure prove that: $AK||BC$
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
102048
Closure of a compact set in Regular space $ X $
138607
Proof that a limit point compact metric space is compact.
80180
Discrete and compact subset must be finite
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
9268
Proving that the Union of Two Compact Sets is Compact
32630
Proving that a set in which any sequence having exactly one accumulation point converges is compact
128835
Compactness of the set of $n \times n$ orthogonal matrices
146146
Proof that a closed subset of a compact space is a compact space
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
51853
$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
114139
Convex Hull of Precompact Subset is Precompact