Why is $(C([a,b]),||\cdot||_{1})$ not complete?
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
96039
Why is $\frac {1\cdot2\cdot3\cdot...\cdot n}{(n+1)(n+2)...(2n)}\le \frac 1 {n+1}$
71392
Is $\operatorname{lcm}(a,\gcd(b,c))=\gcd(\operatorname{lcm}(a,b),\operatorname{lcm}(a,c))$
155063
Is Cl(f(A)) a subset of f(Cl(A))?
131664
Why is any Lebesgue-Stieltjes measure on $(\mathbb{R},\mathcal{B}_\mathbb{R})$ not complete?
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
47838
Lemma 3.3-7 and Theorem 3.6-2 in Kreyszig's "Introductory Functional Analysis With Applications": What if completeness is lost?
111515
Proving that $-a=(-1)\cdot a$
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
44689
Explicit bijection between $[0,1)$ and $(0,1)$
70266
1-1 correspondence between [0,1] and [0,1)
118617
Completeness and Incompleteness
117320
Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
5230
Why can a 1 element set be a member of another set but not a subset of it?