Originally Posted by

**Sogan** Hello,

i have a question about a immersion or submersion.

A function is a immersion/submersion at a point p if its derivative at that point p is injective/surjective.

What __exactly__ does it mean for you that a function is injective/subjective ON ONE POINT? For me this

is senseless, but perhaps you have a definition I don't.

Tonio

I have read that if a function is a immersion/submersion at p, then it is a immersion/submersion in a nbh. of p.

Can you explain me, why there must be a open nbh. s.t. the function is a immersion/submersion for all points in this nbh.?

Regards