Examples 5.2.7(a):
Consider the collection of sets
(0, 1/j) for all j > 0. What is the intersection of
all of these sets ?
The intersection of all intervals (0, 1/j) is empty. To see
this, take any real number x. If
x 
Note that this is an intersection of 'nested' sets, that is sets that are decreasing: every 'next' set is a subset of its predecessor.