Talk:Complex Analysis/Complex Functions/Continuous Functions

The following sentences I have moved here

Note that $$f(z_0)$$ is defined iff $$z_0$$ is an accumulation point of $$\mathfrak{G}$$ belonging to $$\mathfrak{G}$$.

A point in a set is always an accumulation point of that set.

Since this definition assumes that f(z) is finite, we introduce the concept of chordal continuity: a function f is chordally continuous at $$z_0$$ if for any real for any real number $$\epsilon >0$$ we can find a real number $$\delta >0$$ such that $$\chi(f(z)-f(z_0))<\epsilon$$ for all z that satisfy $$\chi(z,z_0)<\delta$$. Note that a function that is continuous at a point is also chordally continuous there, although the converse may not be true (proof).

it is not said what finite is nor what $\chi$ means here.