Closed simple curves in $\mathbb{R}\mathbb{P}^2$

EDIT: The well known Jordan curve theorem says: let $$C\subset S^2$$ be a closed simple curve on the 2-sphere. Then its complement $$S^2\backslash C$$ consists of two connected components, both homeomorphic to discs (in fact it is known that the closure of each component is homeomorphic to the closed disk by Jordan-Schoenflies theorem).

Is there a version of the Jordan theorem for closed simple curves in real projective plane $$\mathbb{R}\mathbb{P}^2$$? (The curve might be assumed to be smoothly imbedded.)

ADDED: Given the comment by HenrikRüping below, I realized that for my purposes it suffices to assume that the homology class of $$C$$ vanishes in $$H_1(\mathbb{R}\mathbb{P}^2,\mathbb{Z}/2\mathbb{Z})$$.
• of course if we look at a closed simple curve representing the generator of $\pi_1$, the complement should have only one connected component homeomorphic to a disc. – HenrikRüping Dec 15 '19 at 18:40
Well, if you take the double cover, under your assumptions the lift is two simple closed curves in $$S^2,$$ the complement of which will be two disks and an annulus, so the original curve bounds a disk on one side.