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How to prove that a topological space is non-hausdorff?
You can check the above conditions and throw-in metrizability as a sufficient--tho not necessary --condition for Hausdorffness.
Still, I think the question is too broad* ; and you may find a better answer if you know how the space is presented/described to you.
*tho, don't get me wrong, I like broads.
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