If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $X$, then $Z$ is compact in $Y$
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
41408
Which of the following sets are compact:
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
146146
Proof that a closed subset of a compact space is a compact space
153573
Counter Example for the union of any number of compact sets is compact in T2-spaces
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
65976
in a topological space only finite subsets are compact sets
64694
$C_{c}(X)$ is complete. then implies that $X$ is compact.
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
79697
If $A$ is a subset of $B$, then the closure of $A$ is contained in the closure of $B$.
4171
If $f$ is locally Lipschitz on $X$ and $X$ is compact, then $f$ is Lipschitz on $X$.
39076
Contraction of compact sets
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.