For the set A = [(-10,0]U(5,7)] ∩ Q.
Find its interior points and limit points.

Question

For the set A = [(-10,0]U(5,7)] ∩ Q.
Find its interior points and limit points.

anonymous · Answer

if it intersect with Q, it is back to itself? that is (-10,0]U(5,7)..

experimentx · Answer

what are the element of Q??

anonymous · Answer

Q is a set of rational numbers

anonymous · Answer

Limit points would be all rational numbers in (-10,0)U(5,7)

anonymous · Answer

No interior points though =)

anonymous · Answer

@SmoothMath  : do you means that the interior point is $$\emptyset$$

experimentx · Answer

http://en.wikipedia.org/wiki/Interior_%28topology%29 "the lower limit topology, then int([0, 1]) = [0, 1) " (-10,0]=> 0 is also interior point. I am not sure .. if the region has be to simply connected.

anonymous · Answer

Yes. That's what I mean.
Consider the definition of an interior point. If x is an interior point of the set, I can find SOME open interval centered at x that is completely contained in the set.
For this set, only rational numbers are included. Think about taking a tiny interval around a number in this set. Will it include any real numbers? If it does, then that interval is not in the set.

anonymous · Answer

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