Lower limit topology

In mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set formula_1 of real numbers; it is different from the standard topology on formula_1 (generated by the open intervals) and has a number of interesting properties. It is the topology generated by the basis of all half-open intervals ["a","b"), where "a" and "b" are real numbers.
The resulting topological space is called the Sorgenfrey line after Robert Sorgenfrey or the arrow and is sometimes written formula_3. Like the Cantor set and the long line, the Sorgenfrey line often serves as a useful counterexample to many otherwise plausible-sounding conjectures in general topology. 
The product of formula_3 with itself is also a useful counterexample, known as the Sorgenfrey plane.
In complete analogy, one can also define the upper limit topology, or left half-open interval topology.