6 The intersection of infinitely many dense open sets may not be dense 5 complete metric space $X$ and nested sequence of closed sets $A_m \subset X$ where $\bigcap_{n=1}^\infty = \emptyset$ 4 Proving $\lim _{n\to \infty }a_{n+1}=\lim _{n\to \infty }b_{n+1}$ where $a_{n+1}=\frac{a_n+b_n}{2}\:$, $b_{n+1}=\sqrt{a_n\cdot \:b_n}$ 3 Character of a solution to a Cauchy problem 3 Groups such that inclusion on collection of all its subgroup is a total order

### Reputation (485)

 +10 Groups such that inclusion on collection of all its subgroup is a total order +10 complete metric space $X$ and nested sequence of closed sets $A_m \subset X$ where $\bigcap_{n=1}^\infty = \emptyset$ +20 Converting problem with norm bound to SOCP problem +10 Fourier Transform - Limit not existing

### Questions (6)

 2 Converting problem with norm bound to SOCP problem 2 Vanishing of a Vector Field 2 Expected time until beating an initial try 1 Reference Request : Quotients of nilpotent groups which are torsion free 1 Unbounded Geodesics and Nonpositive Curvature

### Tags (33)

 12 real-analysis × 5 4 sequences-and-series 11 general-topology × 3 3 group-theory × 3 7 limits × 2 3 abstract-algebra × 3 4 calculus 3 ordinary-differential-equations × 2 4 recurrence-relations 3 divergence-operator

### Bookmarks (4)

 8 Fractions with numerator and denominator both odd 3 Conditional probability for two normal distributed variables. 3 Find all odd positive integers $n$ greater than $1$ such that for any coprime divisors ... 2 Stone Representation Theorem