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From: George Jefferson on 6 Apr 2010 23:36

BTW, if it is any easier one can use C^n->C for the function spaces.
From: William Elliot on 7 Apr 2010 02:13
On Tue, 6 Apr 2010, George Jefferson wrote:

> I can't come up with any non-trivial function space homomorphism between
> f:R^k->R and g:R^i->R. (specifically for k = 1 and i = 2)
>
H(f)(x,y) = f(x)
K(f)(x,y) = f(y)
Z(f)(x,y) = 0 is trivial

H maps f:R -> R to the function h:R^2 -> R, (x,y) -> f(x).
H(f) = p1.(f x g)

for any g:R -> R and
fxg:R^2 -> R^2, (x,y) -> (f(x),g(y)).
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