## 6.4. Topology and Continuity

### Examples 6.4.7(b):

Does the function have
an absolute maximum and minimum on

*[-2, 1]*? How about on the interval*[0, )*?On the other hand, on the unbounded interval [0, ) the function fails to possess both absolute maximum and minimum. While 1 is still the absolute maximum, there no longer is an absolute minimum.

Thus, the boundedness condition in the Max/Min theorem for continuous functions is essential.