Question

Please help me explain why the statement is true: if the intersection of two open intervals is nonempty, then their intersection is an open interval.

Answer 1

there are only two possibilities, one is that interval A is contained in interval B in which case their intersection is A and A is presumed to be open

other possibility is that they overlap, in which case since the endpoint is not included in either interval, the endpoint of the intersection is not as well

i am presuming this is intervals on the real line