Locally Hausdorff not implies Hausdorff

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This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Locally Hausdorff space (?)) need not satisfy the second topological space property (i.e., Hausdorff space (?))
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Statement

A locally Hausdorff space need not be Hausdorff.

Related facts

Proof

An example is the line with two origins, which illustrates the more general fact that a locally Euclidean space need not be Hausdorff, and hence need not be a manifold.