We have , where is the zero map.
Can you transform or/and so their sum will become a function strictly decreasing on and strictly increasing on ? Can be a subgroup?
Okay, Im really confused and in desparate need of help.
I know that the set of functions forms a group under addition.
Now for to be a subgroup of the following conditions have to be met:
(1) For every
(3) For every
But I thought that that the set of functions does not form a group under multiplication, which to me, seems to conflict with condition (1) from above.
Ahhhhhhhhhhh , I think im getting things so confused
(In your post, I think some occurences of should be replaced by )
I guess you think that doesn't satisfy (1), and it is true.
I was trying to give you something easy to visualize in my last post.
For example, let and be the functions defined by:
Are they in ? And their pointwise addition?