Example to show the distance between two closed sets can be 0 even if the two sets are disjoint
127972
Can distance between two closed sets be zero?
52629
Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
33014
Bijection between an open and a closed interval
33310
Proving that the set of limit points of a set is closed
126897
Showing the set $A+B$ is closed.
93606
Showing that $C[0,1]$ is not complete
25874
Showing that a certain map is not flat by explicit counterexample
32912
Getting the difference between two sets
148992
A finite set is closed
55661
Existence of two disjoint closed sets with zero infimal distance
78300
Showing a set is closed other than giving a counterexample?
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
132382
Showing a set is nowhere dense in $C([0,1])$
123090
How to show that disjoint closed sets have disjoint open supersets?
58101
The set of points where two maps agree is closed?
28539
Does any uncountable set contain two disjoint uncountable sets?
153495
Continuous function does not map closed set to closed set