# Definition about the sum of 1-forms

• Oct 26th 2010, 12:27 AM
Sogan
Definition about the sum of 1-forms
Hello,

i have a short question about the sum of two 1-forms.
We have defined a 1-form w by a pair of smooth functions p,q and we write:
w:=p dx + q dy.

Later we have use the sum of two 1-forms $w_1+w_2$, without any definition.

How is the definition of this. Is it just: $
w_1+w_2:= (p_1+p_2) dx + (q_1+q_2) dy
$

if $w_1=p_1 dx + q_1 dy
$

and $w_2=p_2 dx + q_2 dy ?
$

Sorry, if this question is trivial for you, but i'm beginner in topology.

Thank you for helping.
• Oct 26th 2010, 01:57 AM
xxp9
right. the set of all 1-forms is a linear space with dx1, dx2, ..., dxn as the base.
• Oct 26th 2010, 04:49 AM
Sogan
Ok, thanks.

But what do you mean by dx1,...dxn?