Intersection of any number of compact sets is compact.
55648
Intersection of finite number of compact sets is compact?
113922
Proof that the intersection of any finite number of convex sets is a convex set
152193
The intersection of a closure with an open set
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
26919
Intersection of Connected Sets
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
8015
Compact set plus a closed set is a closed set
94485
Limit point compactness implies compactness.
10531
Is the convex hull of a compact set compact?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
111360
Topological spaces in which every proper closed subset is compact
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
115625
Intersection of two open dense sets is dense
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$