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A T1 Space That is Not a T2 Space

Consider the set

Define the topologyon

Sets containing 1 are open if and only if they are the complement of a finite set.

Sets not containing 1 are open when they are open in setr with the usual topology.

Hence, each open set containing 0 is infinite.

Therefore points 0 and 1 cannot be placed in open disjoint sets.

The space is T1 but not T2.

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