Katlus
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### Questions (190)

 12 Prove that every set with more than one element has a permutation without fixed points 10 Difference between ZFC & NBG 9 If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$ 8 Why uniform closure $\mathscr{B}$ of an algebra $\mathscr{A}$ of bounded complex functions is uniformly closed? 8 How do i prove that every open set in $\mathbb{R}^2$ is a union of at most countable open rectangles?

### Reputation (2,440)

 +5 Prove that every set with more than one element has a permutation without fixed points +10 Difference between ZFC & NBG +10 How do i prove that every open set in $\mathbb{R}^2$ is a union of at most countable open rectangles? +5 Counterexample of Compactness

 2 How do i prove that this given set is open? 1 Helly's selection theorem (For sequence of monotonic functions) 1 How do I prove the middle-$\alpha$ cantor set is perfect? 1 Convex and continuity (ZF) 0 Lebesgue integral of simple function

### Tags (37)

 3 general-topology × 47 0 ordinals × 11 2 real-analysis × 85 0 measure-theory × 10 1 axiom-of-choice × 43 0 metric-spaces × 7 0 elementary-set-theory × 35 0 analysis × 7 0 set-theory × 20 0 abstract-algebra × 7

### Account (1)

 Mathematics 2,440 rep 1925