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[SOLVED] example of closed set

dwsmith

Well-known member
Feb 1, 2012
1,673
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
Jan 26, 2012
4,193
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 $\epsilon<1/2$?