Let

be the family of sets

in

such that

is empy or

is finite.

Show that

is a topology on

. By considering the inverse images of closed sets, show that every polynomial function

is

-continuous.

Hey everyone, I was wondering if anyone could assist me with the 2nd part. If

is closed in

then

is the empty set, or A is finite, i.e. A is

or finite.

I don't understand though how

is closed and I would really appreciate some advice here, thank you so much. This would show continuity of the polynomial functions.