Let $\mathcal{C}$ = {$(a,b): - \infty \le a < b \le \infty$}.

Question

Let $\mathcal{C}$ = {$(a,b): - \infty \le a < b \le \infty$}. Is it closed under complementation, countable union, countable increasing unions?

I could show that it is not closed under complementation as $(- \infty, \infty)^c =${$-\infty,\infty$} which is not in $\mathcal{C}$. But what about unions?

Answer 1

Hint: Is $(0,1)\cup(1,2)$ an interval of the form $(a,b)$?