How do I show that if $A$ is compact and $U \supseteq A$ is open, then there is an open $V$ with $A \subseteq V \subseteq \overline{V} \subseteq U$?
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
147914
Closed image of locally compact space
113696
Showing that the unit ball in $(C^\alpha[a, b], \|\cdot\|_\alpha)$ is compact in $(C[a, b], \|\cdot\|_\infty)$
128334
Question regarding open covers in Zariski topology (distinguished opens of affine schemes are quasi-compact)
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
47668
Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
101486
Understanding that $A = \{x\in \ell_2: |x_n| \leq \frac{1}{n}, n = 1,2,...\}$ is compact in $l_2$.
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
73130
A simple question about open set
150379
Perfect Map $p:\ X\to Y$, $Y$ compact implies $X$ compact
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
63701
An example of a regular function over an open set
147331
Compactness and Hausdorffness
106606
How to prove that compact subspaces of the Sorgenfrey line are countable?
28391
Prove the compactness of a set B
148403
Compact space and Hausdorff space