Let be the set of montonic functions . That is, if either

,

or

.

Is a subgroup of under pointwise addition?

Thank-you in advance for any help.

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- March 29th 2009, 06:41 AMwoody198403Sets of Monotonic Functions
Let be the set of montonic functions . That is, if either

,

or

.

Is a subgroup of under pointwise addition?

Thank-you in advance for any help. - March 29th 2009, 09:20 AMclic-clac
Hi

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? - March 31st 2009, 03:43 AMwoody198403Brain Exploding
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

(2)

(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 (Angry), I think im getting things so confused (Headbang) - March 31st 2009, 09:07 AMclic-clac
(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?