show/hide this revision's text 3 rewrote without guess

My guess is

Since now we know that R in your question refers to real line equipped with standard topology. In that case, sheaf cohomology will always have H^i(F) = 0 for i>1 — depending on how you define sheaf cohomology this is a theorem of different difficulty.
show/hide this revision's text 2 left out "obvious" part

My guess is that R in your question refers to real line equipped with standard topology. In that case, sheaf cohomology will always have H^i(F) = 0 for i>1 — depending on how you define sheaf cohomology this may be is a theorem or, if you define it by Cech cocycles, simple consequence of the definitondifferent difficulty.
show/hide this revision's text 1

My guess is that R in your question refers to real line equipped with standard topology. In that case, sheaf cohomology will always have H^i(F) = 0 for i>1 — depending on how you define sheaf cohomology this may be a theorem or, if you define it by Cech cocycles, simple consequence of the definiton.