18 problems.
- Dimension lower bound for the inverse image of a subspace
- Nested closed sets of vanishing diameter in a complete metric space intersect
- Orthogonal idempotents from a direct-sum decomposition into left ideals
- Maximum modulus of a rational function on the closed upper half-plane
- Derivative of the matrix squaring map
- Proper invariant subspaces and factors of the characteristic polynomial
- A finite transitive group action has a derangement
- The contour integral \(\frac1{2\pi i}\int_{|z|=1}\frac{(z+2)^2}{z^2(2z-1)}\,dz\)
- Three-dimensional differentiation-invariant spaces of smooth functions
- A continuous function with a finite limit at infinity is uniformly continuous — Fall 1999 Problem 10; finite limit at infinity implies uniform continuity
- Commuting diagonalizable matrices are simultaneously diagonalizable — Fall 1999 Problem 11; commuting diagonalizable operators are simultaneously diagonalizable
- Bounded holomorphic functions on a disk minus a convergent sequence extend holomorphically
- Degree and automorphism group of \(\mathbb Q(\sqrt[10]{2})\)
- Every infinite closed subset of \(\mathbb R^2\) is the closure of a countable set
- Vanishing traces of the first \(n\) powers force nilpotence
- The integral \(\frac1{2\pi}\int_0^{2\pi}|ae^{i\theta}-b|^{-4}\,d\theta\) for \(0<a<b\)
- Subgroups of \((\QQ,+)\) as countable groups whose finite subsets lie in infinite cyclic subgroups
- Convolution with an integrable function vanishes at infinity