Thread: Topology definition (open/closed)

Is the set from -infinity to +infinity open, closed, neither and/or both?

Hey Bamsefar.

This is an interesting question: I guess one way to look at it is if you can construct a complementary set with respect to the real numbers and the complementary set is the empty set.

So is the empty set open, closed, neither and/or both?

If I'm not mistaken the empty set is both open and closed by definition, which would mean that the answer to my original question is also "both".

Originally Posted by Bamsefar

If I'm not mistaken the empty set is both open and closed by definition, which would mean that the answer to my original question is also "both".

In any topology on a set both are both open and closed.