Editing Metrizable space (section)

===Locally metrizable but not metrizable===

The [[Line with two origins]], also called the ''{{dfn|bug-eyed line}}'' is a [[non-Hausdorff manifold]] (and thus cannot be metrizable). Like all manifolds, it is [[locally homeomorphic]] to [[Euclidean space]] and thus [[locally metrizable space|locally metrizable]] (but not metrizable) and [[Locally Hausdorff space|locally Hausdorff]] (but not [[Hausdorff space|Hausdorff]]). It is also a [[T1 space|T<sub>1</sub>]] [[locally regular space]] but not a [[semiregular space]].

The [[Long line (topology)|long line]] is locally metrizable but not metrizable; in a sense, it is "too long".