Thread: Topology on X

Consider the set

The collection of subsets are

The book says the one point set is not closed because its complement is not open. What is the complement of

Originally Posted by dwsmith

Consider the set
The collection of subsets are
The book says the one point set is not closed because its complement is not open. What is the complement of

Originally Posted by Plato

But that isn't in topology.

Originally Posted by dwsmith

But that isn't in topology.

That is exactly the point.
The complement of is not an open set, not in the topology.
There because the complement of is not open means is not closed.