If $A\subset K$ and $K$ compact, does $\bar A$ compact?
37654
Topology: Example of a compact set but its closure not compact
22854
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
118045
Is the Baire space $\sigma$-compact?
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
148403
Compact space and Hausdorff space
51853
$K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded.
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
73154
Compact subset in colimit of spaces
55648
Intersection of finite number of compact sets is compact?
97951
Is the void set (∅) a proper subset of every set?
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
135157
Totally bounded, complete $\implies$ compact
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$