Give an example of closed, disjoint subsets A and B of the plane R^2 for which d(A,B) = 0
5323
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint
52629
Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
58101
The set of points where two maps agree is closed?
98206
Let $B\subset\mathbb{R}^d$ be closed and $z\in\mathbb{R}^d$, show that there is $b_0\in B$ such that $\delta(z,B)=\|z-b_0\|$.
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
35305
Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
156101
Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
116378
Nonhomeomorphic subsets of the plane
158569
Proving a particular subset of $R^n$ is closed
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
116806
Find the weak sequential closure of a set in $L^2(-\pi,\pi)$
109462
Looking for a counter example for non-connected intersection of descending chain of closed connected sets
143269
Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$
16582
Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions
143100
Identify the plane defined by $|z-2i| = 2|z+3|$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$