## 6.4. Topology and Continuity

### Examples 6.4.5(a):

*[-2, 1]*is

*[1/5, 1]*. In particular, the image of a compact set is compact.

To find a closed set whose image is not closed we must consider an unbounded set. Otherwise, a closed and bounded set is compact, and since the image of a compact set under continuous functions is compact, it is in particular closed again.

But if we look at the closed, unbounded set
*[0, )*,
we see that the image of that set under the above function is
the set *(0, 1]*, which is not closed.