Compact set in $\mathbb{R}^n$ and the finite intersection property
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
9268
Proving that the Union of Two Compact Sets is Compact
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
106455
intersection of infinite collection of finite sets?
69367
covering map with finite fibres and preimage of a compact set
158569
Proving a particular subset of $R^n$ is closed
56728
Question about limit points of a Subset of $\mathbb{R}$
44623
Closed set as a countable intersection of open sets
74498
Smallest dense subset of $\mathbb{R}$
78117
Closed property of nonempty finite set
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
63529
How to show that this set is compact in $\ell^2$
12436
The cardinality of the set of all finite subsets of an infinite set
82474
Isometries of $\mathbb{R}^n$