# Let f be an embedding of disk $D$ in Real Projective plane $P$. Show that $P- int(f(D))$ is homeomorphic to Mobius strip.

This question is partially answered here: How to see the real projective plane is a Möbius band glued to a disk?

In that answer it is shown that for a very specific embadding $$f: D \rightarrow P$$, space $$P - int(D)$$ is homeomorphic to Mobious strip and it can be (rigorously) proved constructively.

I want to show that that is the case for every embedding.

I would like to somehow use Jordan curve theorem and Schoenflies theorem but I must just stuck on how to prove that for a non specific embedding of a disk $$D$$.

Anyone any ideas?

I am hesitant to use the Jordan curve theorem here but perhaps it is possible. Instead what I would use is the important fact that the space $$Emb(D^n , M)$$ is equivalent to $$Fr(M)$$, the total space of the fiber bundle over $$M$$ where the fiber over $$x$$ is the space of bases of the tangent bundle. Here $$M$$ is n-dimensional. This equivalence just comes from pushing forward the standard basis along the derivative.