My understanding is that a set is simply-connected if every closed curve in the set can be continuously contracted to a point without leaving the set.
In this case, we have the vector field $F = \left( 3x^2\ln(z), 16y^7z^4, \dfrac{x^3}{z} + 8y^8z^3 \right)$. However, it seems to me that this set isn't simply connected, since we have that $z > 0$? Given this restriction in the domain, wouldn't we have "holes"?
I would greatly appreciate it if people could please take the time to clarify this. If the set is simply-connected, then which part of my understanding of this concept is incorrect?