8.4 Continuous Functions
What was done in one variable calculus for scalar functions is generalized here to include the case of a
vector valued function of possibly many variables.
Definition 8.4.1 A function f : D
⊆ ℝp → ℝq is continuous at x ∈ D
if for each ε >
0 there exists
0 such that whenever y ∈ D
it follows that
f is continuous if it is continuous at every point of D
Note the total similarity to the scalar valued case.