Prove that the topology T on X is the discrete Topology if and only if {x} T for all x X.
I know what the definition for discrete topology is but im having a hard time prove this.
Recall that a topology is closed under finite intersection and arbitrary union.
If is a topology on having the property that
then if are two points in what is ?
What is ?
If
You said that you know the definition of discrete topology.
What does the above show about ?