I am trying to understand what the definition of smooth boundary is. From the following lectures notes on analysis 3 :
So intuitively, a smooth boundary ( in this case , it is a $C^1$ boundary) should have no edges and corners. So I think condition $b$ takes care of that. But why do we have condition $a$?
Also why does having a smooth boundary imply $\Omega$ has the interior ball property? The interior ball property is : for each $x\in \partial \Omega$, there exists a ball $B \subset \Omega$ such that $x\in \partial B$.
Intuitively, this seems like it should be true, but I don't see how we get from the definition of smooth bondary to this.