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Currently, this entry only considers functions R-> R and C->C. Would
it be possible to generalize this to functions from X-> R(or C) where
X is a topological space? (The theorem holds under this assumption.)

For clarity, I would write out the limits on both sides
of the equility sign in the claims. That is, I would leave out the
(unnecessary notation a,b). These are usually introduced when proving
the claim. However, notation for the proof should not be introduced
in the theorem statement. However, this is a matter of taste.

For example,

Suppose $
1) lim_{x\to x_0} c = c when $c$ is a constant,
2) lim_.. (f(x)+g(x)) = lim f(x) + lim g(x), where f,g are functions
3) If f\colon X\to Y is a continuous function between topological
spaces X,Y, and $g$ is a function Y\to C, then
lim g\circ f(x) = g(lim f(x))

Additional property:
If $X$ is an interval of R, and the one-sided limits
lim_{x\to x_0+} f(x), lim_{x\to x_0-} f(x)
exists and are equal,
then the limit lim_{x\to x_0} f(x) exists and is equal to
the one-sided limits.

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?): 
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