Strategy to prove a set is compact. Case: $S=\{0\}\cup\bigcup_\limits{i=1}^{\infty}\{\frac{1}{n}\}$
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
141260
Prove using the formal definition of a limit that
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
117781
Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
48783
Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
77286
Proving set theory question
77480
Is the set $S=\left\{\left(z_1,z_2\right)\in \mathbb C\times \mathbb C:z_1^2+z_2^2=1\right\}.$ compact?
151852
How to prove $A \subset B \iff A \cup B = B$
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
37654
Topology: Example of a compact set but its closure not compact
76918
Construct a compact set of real numbers whose limit points form a countable set.
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
32630
Proving that a set in which any sequence having exactly one accumulation point converges is compact
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable