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Hausdorff space

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8. Let X be any set of infinite cardinality. Consider the set A = { A SUBSET X : X - A is finite } UNION { PHI , X }.

a) Prove that A is a topology on X.
b) Describe the neighborhoods of a point P BELONGING_TO X.
c) Is X a Hausdorff space with this topology?

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Solution Summary

Hausdorff space is clearly explored in this case.

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