30 are closed sets in the particular point topology PPX p on

30. are closed sets in the particular point topology PPX p on a set x? Which sets (See Exercise 1.7.)

Solution

By defnition of closed set we know

A set S is closed under a topology if its complement is open.

Now as in PPX_P

We have A ( a subset of X) is open in PPX_P if A contains p,

So the sets which are closed in PPX_P are those which do not contain p