Show that the closed ball around some point in a metric space is a closed set.
35573
A closed ball in a metric space is a closed set
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
43248
Closure of a Ball is Contained in Closed Ball (usual metric)
126897
Showing the set $A+B$ is closed.
13848
Showing that if a subset of a complete metric space is closed, it is also complete
132641
Proving that Euclidean Space is a complete metric space
144383
The closure of a connected set in a topological space is connected
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
44623
Closed set as a countable intersection of open sets
112303
Distances between closed sets on metric spaces
23845
How to prove the continuity of the metric function?
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
24050
Characterization of the Closure of a Set
778
For $x∈\mathbb{R}^n$ , let $B(x,r)$ denote the closed ball in $\mathbb{R}^n$(with Euclidean norm) of radius $r$ centered at $x$
144400
Are compact subsets of metric spaces closed and bounded?
42638
Showing that a function $f$ has a unique fixed point in a metric space.