I was reading definition of surface in differential geometry book which defined as follows
A subset $S\subset \mathbb R^3$ is regular surface if $\forall p\in S $ there is open set in S such that $p\in V $ and $\exists \phi :U\to V\in S$ where U is open set in $\mathbb R^2 $ such that map is surjective , smooth and homeomorphism with image and also $\forall q\in U, dX_q:\mathbb R^2\to \mathbb R^3$ is injective
TO better understand cocept I wanted to know counterexample of regular surface.
Please Help me
Any Help will be appreciated