How to prove $C_{c}^{\infty}[a,b]$ a complete metric space
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
133504
Suppose $X$ is a metric space and $S \subseteq X.$ Then, $S^o=\{x \in X~|~dist(x,S^c)>0\}$.
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
144112
Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
134601
whether they are complete metric space
42638
Showing that a function $f$ has a unique fixed point in a metric space.
16060
Showing this metric space is complete
157753
Show that any set in a metric space can be written as the intersection of open sets
138607
Proof that a limit point compact metric space is compact.
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
35652
Every compact metric space is complete
80276
Metric Space & Cauchy Sequence
70106
diameter on a compact metric space
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
146485
Prove that the product space is a metric space.
28391
Prove the compactness of a set B
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.