A point in a closed set in Euclidean Space
112303
Distances between closed sets on metric spaces
111561
Distance of a point to a subset.
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
49721
Prove the empty set is closed for a metric space (X,d).
22558
Vitali-type set with given outer measure
24266
Accumulation points of the set $S=\{(\frac {1} {n}, \frac {1} {m}) \space m, n \in \mathbb N\}$
19289
complement of a set and its measure
155004
Maximal points on an $n$-dimensional ellipsoid
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
49374
Closure of a subset in a metric space
42494
The boundary is a closed set
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
152976
Real Analysis: open and closed sets
27652
metric on the Euclidean Group
30572
Intersection of nested closed bounded convex sets in Euclidean space
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
324
Show uncountable set of real numbers has a point of accumulation