What is a 'basic region' in calculus? My friend told me that a basic region is defined as a connected set in which the total boundary consists of a finite number of continuous curve of the form $y=f(x)$ or of the form $x=g(y)$. Is the above definition correct?
As far as I am aware, "basic region" is not a standard mathematical term in reference to calculus.
However, in this economics text, we find the definition
"A basic region is a connected set in which the total boundary consists of a ﬁnite number of continuous arcs of the form $x_2=\phi(x_1),x_1=\psi(x_2)$."
Carefully note that this is not the same as what your friend said, and is actually not even close. It's easy to see that your friend's definition allows for self-intersecting curves, while this one does not. The difference between the and and the or here it critical.