Show that the metric $d_1$ on $C([0,1])$ does not give rise to a complete metric space.
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
49374
Closure of a subset in a metric space
23845
How to prove the continuity of the metric function?
35573
A closed ball in a metric space is a closed set
86717
Completeness of $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle$
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
80276
Metric Space & Cauchy Sequence
13848
Showing that if a subset of a complete metric space is closed, it is also complete
142901
"The closure of the unit ball of $C^1[0, 1]$ in $C[0, 1]$" and its compactness
137881
A not complete metric space?
18040
Show that a compact metric space is bounded
15480
Open set in a metric space is union of closed sets
140692
Existence of a complete metric on $(0,1)$
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
132382
Showing a set is nowhere dense in $C([0,1])$