# doubt on representation theorem for open sets in R

statement says that every non empty open set in R is union of countable collection of pairwise disjoint open intervals so if my interval is (0,1) then is it's representation according to above theorem is itself (0,1)?because if i broke down it into open sub-intervals like union of (0,0.5) and (0.5,1),we will miss 0.5?so am i right?

• English sentences start with capital letters. – Michael Greinecker Oct 25 '17 at 8:21
• "I" will keep this in mind from now onwards:) – Believer Oct 25 '17 at 8:26

If your interval is $(0,1)$ then $\{(0,1)\}$ is exactly its representation.