Show that any ball (open or closed) in $\mathbb{R}^n$ is a convex set.
40438
Proving that closed (and open) balls are convex
18763
injective holomorphic function on a convex set
28511
Hypervolume of a $N$-dimensional ball in $p$-norm
14448
Elementary proof that $|x|^p$ is convex.
52231
Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex
121095
Is convex hull of a finite set of points in $\mathbb R^2$ closed?
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
144353
A closed ball in a metric space is closed
150727
Characterization convex function.
72468
Open and closed balls in $C[a,b]$
30572
Intersection of nested closed bounded convex sets in Euclidean space
53132
A convex subset of a set has 'smaller' boundary than the set?
99678
Is a sphere a closed set?
36371
Exercise on convex functions
57514
The Minkowski sum of two convex sets is convex
6491
Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$