In a metric space, is the dilation of a closed set closed?
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
33310
Proving that the set of limit points of a set is closed
28804
No. of possible dense subsets of a metric space
144400
Are compact subsets of metric spaces closed and bounded?
112303
Distances between closed sets on metric spaces
158155
Is set of isolated points of S closed?
61930
Intersection of Closed and Compact Set is Closed
42494
The boundary is a closed set
27517
Isometry in compact metric spaces
95831
Compactness and sequential compactness in metric spaces
138607
Proof that a limit point compact metric space is compact.
36237
Closed set mapped to itself in a compact Hausdorff space
55614
Prove that a set consisting of a sequence and its limit point is closed
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
13848
Showing that if a subset of a complete metric space is closed, it is also complete
45581
Is the distance function in a metric space (uniformly) continuous?
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?