Could someone explain to me this example? I know all the basis and definitions but I am new to calculation of cohomology group

here is the example

http://i51.tinypic.com/wb7609.jpg
Why $\displaystyle Z^{k}= \begin{cases} 0 for \mathbb{R} , k=0\\ 0 , k>0\end{cases}$?? why do we get a real numbers and then we get just 0?

and then boundary group$\displaystyle B^{k}(M)=0$ I guess that it is because a point does not have a boundary, is it correct and finally how did they get the cohomology group? how did they obtain again R and 0?

Thank you