Ordered sets have a natural topology generated by the open intervals. This tag is meant for questions about this topology.
Given a linearly ordered set $(X,<)$, there is a natural topology defined on $X$ from $\lt$, whose basic open sets are of the form $(x,y)$ where $x,y\in X\cup\{\pm\infty\}$ (where $\pm\infty$ denote the unbounded rays, if there are such rays).
Spaces which have a topology generated by a linear order are sometimes referred to as LOTS (Linearly Ordered Topological Space).
Some examples include:
- The real numbers.
- Ordinal spaces.
- The long line.
