TITLE: example of a presheaf
QUESTION [9 upvotes]: I'm now trying to understand some of category theory, I think I can understand the concept of sheaf but I can not understand the difference between sheaves and presheaves.
I asked someones about it and they told me that it could be helpful if I can find an example of a presheaf that does not be a sheaf in a topology space of 3 points with the discrete topology.
But I have not idea of what this could be. So any help will be very appreciated.
Thanks.

REPLY [3 votes]: Consider the space $\mathbb R$ and the sheaf of sets $F$ such that for each open set $U$ the set $F(U)$ is the set of constant functions whose integral is at most $1$.
Is it a sheaf?