Continuity in a point in a metric space
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
84791
Is every connected metric space with at least two points uncountable?
50677
Is this metric space incomplete?
138607
Proof that a limit point compact metric space is compact.
106256
Continuous mapping on a compact metric space is uniformly continuous
83159
Defining a metric space
62334
Continuity and Joint Continuity
76351
Equivalence of continuity definitions
27517
Isometry in compact metric spaces
17234
Show that a continuous function has a fixed point
136583
Infimum is a continuous function, compact set
152493
Is an expanding map on a compact metric space continuous?
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
126842
Fixed point in a continuous function
157753
Show that any set in a metric space can be written as the intersection of open sets
74607
Variation of the metric with respect to the metric
90628
The metric spaces are Tychonoff spaces