Any set of $\mathbb R$ is open iff it is the union of disjoint open intervals

Asked Feb 18 '19 at 23:40

Active Feb 19 '19 at 00:34

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I am starting in my studies on topology and I am having really big troubles with this kind of stuff

I have $(\mathbb R, \tau_u)$, and I have to prove that $A \in \tau_u$ iff $A=\uplus_{i\in I}]a_i, b_i[$

If someone could help me with well-structured demostration of this, I would really appreciate it.

edited Feb 19 '19 at 00:34

asked Feb 18 '19 at 23:40

Ray Romero

You start by showing that a connected open subset is an open interval. Then it follows since every subset is a disjoint union of its connected components. – freakish Feb 18 '19 at 23:46
The problem statement should also be stated in the body of the question, not just in the title. – user159517 Feb 18 '19 at 23:55

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