right 1∉(0,1), so you cannot find any ε-neighborhood of 1 contained within the set (0,1)
The symbol you used here didn't show up on my reader. If is "intersection", then Z intersect R is just Z (which is a subset of R) and that is not open. However on the other problems you seem to be talking about "union". If this is "union", then Z union R is all of R and that is open.
