I read on the page Why are smooth manifolds defined to be paracompact? in one of the answers that every one dimensional complex manifold is automatically paracompact, i.e. there is no complex analogue to the real long line. My problem: I cant find any book or paper explaining me why this should be the case. In most textbooks, a complex manifold is defined to be paracompact even if this was not necessary in this case.
So: Why is every one dimensional Complex Manifold paracompact?
