yeah, the only way I could think to solve this was by eliminating II) and noticing from the choices that the answer has to be b. However, going back and looking at it I still don't see how I) can be eliminated, I think there is a problem with op's proof that
. op splits it up into the cases
but we can't conclude
. For example, under the indiscrete topology,
is the entire set.
Am I right here, and if so does anyone know of a proper proof for I)?