Open and connected set in metric space
13468
When does open and connected imply path-connected?
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
134601
whether they are complete metric space
59654
Show that in a discrete metric space, every subset is both open and closed.
49721
Prove the empty set is closed for a metric space (X,d).
128897
Bounded sequence in a metric space
6415
Distance function is continuous in topology induced by the metric
99236
Interior of closure of an open set
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
83159
Defining a metric space
135315
Proving whether a function on the set of real sequences is a metric
93623
Showing that every connected open set in a locally path connected space is path connected
125580
Proving that every countable metric space is disconnected?
144400
Are compact subsets of metric spaces closed and bounded?
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
111119
Distance between any two points in a compact metric space
157572
The distance between two sets inside euclidean space