>>9320664What is a curve ? How do you measure the curvature of a curve ? Why do simple plane curves separate the plane in two regions ? How would you prove this for a convex polygon ?
Compare the length of a simple closed curve and its area.
Why can't R^n be homeomorphic to R^m if m <> n ? Can GL(n,K) be isomorphic to GL(m,K) if m <> n ? How about GL(n,K) and GL(m,L) for different fields ?
Are two compact convex sets with nonempty interior homeomorphic in R^n ?
Does a group with order divisible by d have a subgroup of order d ? What conditions can be put in order for this to be the case ?
Let G be a finite group acting on a finitely generated K-algebra R. Is the algebra R^G of invariants finitely generated ? What if the group G is infinite ?
Is a subalgebra of a finitely generated algebra finitely generated ?
