Re: Sheaves and the empty set
- From: Jose Capco <cliomseerg@xxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: 18 May 2007 04:23:01 -0700
On May 18, 12:37 pm, Kira Yamato <kira...@xxxxxxxxxxxxx> wrote:
On 2007-05-18 04:53:33 -0400, Jose Capco
<cliomse...@xxxxxxxxxxxxxxxxxxxxxxxxx> said:
Dear NG,
We know very well that if F is a sheaf of rings/groups, then
F(emptyset)=the zero ring/groups..
Suppose X is any topological space. For every open set U in X, define
F(U) = Z
where Z is the ring of integers. Define all restriction maps to be the
identity map on Z.
Is F a sheaf?
-
Like I said, F(emptyset) must be the zero ring if F were a sheaf.. so
this is not a sheaf!
.
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