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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?

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  • $\begingroup$ English sentences start with capital letters. $\endgroup$ – Michael Greinecker Oct 25 '17 at 8:21
  • $\begingroup$ "I" will keep this in mind from now onwards:) $\endgroup$ – Believer Oct 25 '17 at 8:26
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If your interval is $(0,1)$ then $\{(0,1)\}$ is exactly its representation.

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