# [SOLVED]example of closed set

#### dwsmith

##### Well-known member
Given an example of a set $S$ which is closed but not bounded and exhibit a countable open covering $F$ such that no finite subset of $F$ covers $S$.

The set of integers. Since it is a set of points, each point is closed. How would I show a countable covering.

#### Ackbach

##### Indicium Physicus
Staff member
Given an example of a set $S$ which is closed but not bounded and exhibit a countable open covering $F$ such that no finite subset of $F$ covers $S$.

The set of integers. Since it is a set of points, each point is closed. How would I show a countable covering.
How about a small $\epsilon$ interval about each integer, with $\epsilon<1/2$?