Is the set $\{f = \cos(nx) : n=1, ... ,\infty \}$ closed?
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
46698
Showing a set is closed under inverses
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
22391
Is the set of all pairs of real numbers uncountable?
97373
Is whether a set is closed or not a local property?
117257
Proving the supremum of the set {$\cos (1/x)$} is 1
79419
Is $\sin \infty$ an indeterminate form?
36315
Is $[0,1]$ a countable disjoint union of closed sets?
158523
Topology: Proof that a finitely generated cone is closed
26541
Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
107976
Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$
28683
Sum of two closed sets in $\mathbb R$ is closed?
42494
The boundary is a closed set
10180
How to prove that this set is closed?
158569
Proving a particular subset of $R^n$ is closed
121304
Is the set of polynomials of degree less than or equal to $n$ closed?
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X