Open/Closed value of unions of Open/Close intervals. I hope I do not make a duplicate here but I couldn't find this question on here nor a clear answer on the internet.
So let's say I have two intervals, $A$ and $B$.
Let's define $C$ as the union of $A$ and $B$.
Is there some sort of table showing the Open/Closed value of $C$ depending on $A$'s and $B$'s Open/Closed values?
Thank you in advance
 A: The union of two closed sets is always closed, and closed intervals are closed sets, so the union of two closed intervals is a closed set. (It need not be an interval, of course.) The union of open sets is always open, and open intervals are open sets, so the union of two open intervals is open (though again it need not be an interval). The union of an open interval and a closed interval may be open, closed, or neither. Suppose that $A$ is an open interval and $B$ a closed interval. Then $A\cup B$ is


*

*open if $B\subseteq A$, so that $A\cup B=A$;  

*closed if $A\subseteq B$, so that $A\cup B=B$; and  

*neither open nor closed in all other cases.

A: Finite unions of closed intervals are closed, but not infinite ones, arbitrary unions of open intervals are open. The union of open and closed intervals could be open, closed, half open and half closed (clopen), or both open and closed.
Examples:
Finite union of closed sets, $[1,2]\cup[2,3]=[1,3]$.
Infinite union of closed sets $\cup_{n\in\mathbb N}[-n,n]=\mathbb R$.
Union of open and closed intervals:
$(1,2)\cup[3/2,7/4] = (1,2)$
$(1,2)\cup[1,2] = [1,2]$
$(1,2)\cup[3/2,2] = (1,2]$
$(1,2)\cup[3,4]$
$(\cup_{n\in \mathbb N}(-n,n))\cup(\cup_{n \in\mathbb N}[-n,n])=\mathbb R$
Note that $\mathbb R$ is both open and closed.
