Construct a sequence of compacts sets E sub n, such that E1 is in E2 is in E3, etc.
Construct a sequence of compacts sets E sub n, such that E1 is in E2 is in E3, etc. and E n is the union of 2 to the n intervals, each of length 3 to the negative n. The infinite intersection of these E n's forms a compact non- empty set. In fact, this set contains uncountably many points but is still of Lebesgue measure zero. FTP, name this set found by repeatedly removing the middle third of intervals named for its discoverer, the father of set theory.
Construct a sequence of compacts sets E sub n, such that E1 is in E2 is in E3, etc.
{Cantor} set