# Help on smooth manifold!

• April 24th 2012, 06:15 PM
ljwrr1990
Help on smooth manifold!
Why f: R -> R^2 by f(t) = (t^2, t^3) is not a smooth manifold? Just learned the concept of smooth manifold. Really confused about it.
• April 29th 2012, 12:32 AM
Rebesques
Re: Help on smooth manifold!
We cannot find a well defined tangent space at t=0.
• May 11th 2012, 01:13 PM
mastermind2007
Re: Help on smooth manifold!
It's because the inverse function is not differentiable at the point x = 0.
A smooth manifold M is a topological space where for every x in M there is a diffeomorphism $f: M \supseteq U \rightarrow V \subseteq \mathbb{R}^n \ with \ x \in U$ (which means that for every open subset of M there is a chart (=diffeomorphism) that maps U to an open subset of $\mathbb{R}^n$).