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 , without any definition.

How is the definition of this. Is it just:
if
and

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

Thank you for helping.

right. the set of all 1-forms is a linear space with dx1, dx2, ..., dxn as the base.

Ok, thanks.

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