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Math Help - Definition about the sum of 1-forms

  1. #1
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    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:  <br />
w_1+w_2:= (p_1+p_2) dx + (q_1+q_2) dy<br />
    if  w_1=p_1 dx + q_1 dy <br />
    and  w_2=p_2 dx + q_2 dy ?<br />

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

    Thank you for helping.
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  2. #2
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    right. the set of all 1-forms is a linear space with dx1, dx2, ..., dxn as the base.
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  3. #3
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    Ok, thanks.

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