orientability of riemann surface Could any one tell me about the orientability of riemann surfaces?
well, Holomorphic maps between two open sets of complex plane preserves orientation of the plane,I mean conformal property of holomorphic map implies that the local angles are preserved and in particular right angles are preserved, therefore the local notions of "clockwise" and "anticlockwise" for small circles are preserved. can we transform this idea to abstract riemann surfaces?
thank you for your comments

Every coordinate-change of a holomorphic atlas is by definition a bi-holomorphism between opens of $\mathbb{C}^n$, i.e. its derivative (tangent map) is a $\mathbb{C}$-linear isomorphism of $\mathbb{R}^{2n}$, hence has positive determinant.
($n=1$ for a Riemann surface)
