It is a known fact that real numbers are locally compact and rationals are not with respect to the topology inherited from R.
What about irrationals?are they locally compact?
It is a known fact that real numbers are locally compact and rationals are not with respect to the topology inherited from R.
What about irrationals?are they locally compact?
Nope, the irrationals are not locally compact. What can you say about compact sets in the topology on the irrationals? What would happen if such a compact set contained an open neighborhood of a point? (Note that the irrationals are Hausdorff, so compact would imply closed).