If A and B are sets where B has the folowing binary operation defined on it.
BxB -> B
(b,b') -> b*b'
Then given 2 maps, f,g contained in Map(A,B) we get another map f*g contained in Map(A,B) by setting
Map(A,B)xMap(A,B) -> Map(A,B)
(f,g) -> f*g
Of particular importance is the case A=B=R (reals) and it is usual to refer to f and g as functions in this case. Then the addition and multiplication on R induce pointwise addition and multiplication on Map(R,R):
f+g: R -> R
a -> f(a) + g(a)
f.g: R -> R
a -> f(a)g(a)
Can anyone explain whats going on here? I don't understand how maps can be contained in other maps nor the whole pointwise thing.
PS does anyone happen to know if you can write greek characters on a keyboard using alt+ number codes as you can with other european characters?