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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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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