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

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- Oct 13th 2012, 03:35 AMBamsefarTopology definition (open/closed)
Is the set from -infinity to +infinity open, closed, neither and/or both?

- Oct 13th 2012, 03:45 AMchiroRe: Topology definition (open/closed)
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? - Oct 13th 2012, 04:04 AMBamsefarRe: Topology definition (open/closed)
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".

- Oct 13th 2012, 04:19 AMPlatoRe: Topology definition (open/closed)