Question: Verify the properties (left(mathscr{O}_{1}ight))-( (left.mathscr{O}_{3}ight)) for open sets in (mathbb{R}^{n}). Is (mathscr{O}) a (sigma)-algebra?

Verify the properties $\left(\mathscr{O}_{1}ight)$-( $\left.\mathscr{O}_{3}ight)$ for open sets in $\mathbb{R}^{n}$. Is $\mathscr{O}$ a $\sigma$-algebra?

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