finding a normal domain that is not convex.
I thought of this: $\{(x,y) | 4
Does anybody see how to parametrize? Since I believe that if it is parametrizable then it is also normal. Please, do show me the right path.
Definition:
A domain $A\subset \mathbb{R}^{2}$ is a normal domain, if there are piecewise continuously differentiable functions $\alpha_{1},\alpha_{2} : [c,d] \rightarrow \mathbb{R}$ and $\beta_{1}, \beta_{2} : [a,b] \rightarrow \mathbb{R}$ such that : $ A=\{(x,y) | a < x < b, \beta_{1}(x) < y < \beta_{2}(x) \} = \{(x,y) | \alpha_{1}(y) < x < \alpha_{2} (y ) , c< y < d\}$