For ten points, identify this elementary result from real analysis which says that any continuous function from a closed and bounded set to the real numbers has both a minimum and maximum.
One result with this name is also known as the Fisher-Tippett-Gnedenko theorem, and states that certain limit distributions must belong to one of three families of distributions. This result is used to prove Rolle's theorem, because in that case it requires either that the function be constant, or that at some point it has derivative zero. This result follows from the statement that closed and bounded sets   map to closed and bounded sets. For ten points, identify this elementary result from real analysis which says that any continuous function from a closed and bounded set to the real numbers has both a minimum and maximum.
One result with this name is also known as the Fisher-Tippett-Gnedenko theorem, and states that certain limit distributions must belong to one of three families of distributions.
extreme value theorem