In topology, the **long line** is a topological space analogous to the real line, but much longer. Because it behaves locally just like the real line, but has different large-scale properties, it serves as one of the basic counterexamples of topology.

We start with the first uncountable ordinal ω_{1}. This is a totally ordered set, and the cartesian product ω_{1} × [0, 1) becomes a totally ordered set if we use the lexicographic or dictionary order [1]. The long line *L* is defined as ω_{1} × [0, 1) with the order topology arising from this total order. That is, it consists of an uncountable number of copies of [0, 1) 'pasted together' end-to-end. Compare this with the real interval [0, ∞), which can be viewed as a *countable* number of copies of [0, 1) pasted together end-to-end. A related space, the **extended long line**, *L**, is obtained by adjoining an additional element to the end of *L*.

Both *L* and *L** are normal Hausdorff spaces because they are order topologies. Both of them have the same cardinality as the real line, yet they are 'much longer'.
Both of them are locally compact. Neither of them is metrisable.

The long line *L* is not paracompact. It is path-connected and simply connected but not contractible. *L* is a one-dimensional topological manifold with boundary. *L* is first countable but not second countable.

The extended long line *L** is compact; it is the one-point compactification of *L*. It is also connected, but not path-connected because the long line is 'too long' to be covered by a path, which is an image of an interval. *L** is not a manifold and is not first countable.