Thanks for the comments, I lack some context for some of them (which sentence you refer to):
locally analytic branches?
yab is well defined on all C, sure
for the [a,b], (a,b), ]a,b[ I may have made mistakes but open or closed usually depend on the function being holomorphic at the points (fab is, yab not)
Thanks for the comments, I lack some context for some of them (which sentence you refer to):