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.

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- January 11th 2009, 12:17 PMflamingDiscrete Topology Question
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. - January 11th 2009, 01:08 PMPlato
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 ?