See links below for reference.

We call the function everywhere continuous, or simply continuous, if it is continuous at every point of its domain. More generally, we say that a function is continuous on some ***subset*** of its domain if it is continuous at every point of that subset.

http://www.answers.com/topic/continuous-function

Definition

A real valued function f defined on a **subset** S of R is said to be continuous if it is continuous at all points of S.

There is a very similar definition for complex valued functions: ... ***Continuity of
complex functions*** is formally the same as in the case of real functions, ...
http://math.fullerton.edu/mathews/c2002/ca0204.html
Introduction to Complex Analysis
limit and ***continuity***, derivative and integral of ***complex valued functions***.
... We will also examine various applications of complex valued functions, ...
http://www.math.umb.edu/~lam/Math 358.htm

Sint 2 notiuni diferite si le-am despartit cu numere
Ptr. primul se mai poate si sectionally continuous functions

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Note added at 8 hrs 17 mins (2005-07-17 10:46:30 GMT)
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Am vazut ca alte raspunsuri au folosit complex-valued functions. Si asta ar fi potrivit, numai ca s-ar putea intelege ca functia are numai valori complexe, pe cand textul original nu exclude posibilitatea ca o parte din valori sa fie complexe si o alta parte nu.