On Fri, May 30, 2014 at 10:52 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
(5) Andy's counter-example --- a straight line of zeros within an infinite strip R --- I did foresee, but ignored on the grounds that it can be fixed by compactification. Adjoin a complex point or projective line at infinity: the boundary of R then includes points at infinity where the line meets it.
If you know the conjecture you're making is false, and have a patched-up version of the conjecture that's actually what you're asking about, I'd find it more useful if you actually stated the patched-up conjecture, rather than having us each guess what patching up you intend. So the question you were asking about R2, you are actually meaning to ask about some compactification of R2. Would that be the one-point compactification? or RP2, the real projective plane? Or some other compactification? Andy