Locally Hausdorff space

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In mathematics, in the field of topology, a topological space is said to be locally Hausdorff if every point has an open neighbourhood that is Hausdorff under the subspace topology.

Here are some facts:

• Every Hausdorff space is locally Hausdorff.
• Every locally Hausdorff space is T1.
• There are locally Hausdorff spaces where a sequence has more than one limit. This can never happen for a Hausdorff space.
• The etale space for the sheaf of differentiable functions on a differential manifold is not Hausdorff, but it is locally Hausdorff.

[edit] See also

Hausdorff space