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some issues remain

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some issues remain

1) The definition is still problematic. The problem is
that you first fix S to be one particular surface,
and then you take limits over it.

The right way to write this would be

(curl F)(p) = lim_{V->0} .... ,

where V is the volume of a closed surface S enclosing the
point p.

2) Just a few extra words about the scale factors will go a long
way to help the reader (saving them clicking effort, and adding
very little text) Something like

where h_i = d/dxi * d/dxi, i=1,2,3 are the coordinate system
scale factors.

3) The sentence

It should be clear from the above discussion that
curl itself is a vector field.

is poor writing style. You are the one giving the definition,
and it isn't fair to ask the poor readers to guess what it is
you are trying to define. Also, you are still not upfront
about your hypotheses.

Suggestion: right of the bat say:

Let V be a vector field in 3-dimensional Euclidean space.
The curl of V, written curl(V), is another vector field
defined by ....

something like that

Parting words from the person who closed the correction: 
Status: Accepted
Reference to the user who closed the correction.: 
Reference to the article this correction is about: 
Status of the article (was it accepted?): 
Status of the article (is it closed?): 
What kind of correction is this: 

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