Show that $C([a,b])$ is complete
61202
Show that $C[a,b]$ is a complete space under the metric $d(f,g)=\sup_{t\in [a,b]}|f(t)-g(t)|$.
100362
Codomain of function complete implies function space complete
2575
Showing that $\mathbb{R}$ is connected
77791
Proving an inclusion related to algebraic sets and interpreting it
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
61640
Prove c exists for f:[0,1] -> R
155063
Is Cl(f(A)) a subset of f(Cl(A))?
5149
Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
72468
Open and closed balls in $C[a,b]$
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
32910
Completion and algebraic closure commutable
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
13848
Showing that if a subset of a complete metric space is closed, it is also complete