Sorgenfrey line

Definition
The Sorgenfrey line is defined as follows: as a set, it is the real line, and its basis of open sets is taken as all the right-open, left-closed intervals, viz., sets of the form $$[a,b)$$. Equivalently, we can say that it is obtained by giving the lower limit topology corresponding to the usual ordering on the real line.

The product of two copies of the Sorgenfrey line is the Sorgenfrey plane, which is not normal. This gives an example of the fact that a product of two normal spaces need not be normal.

Textbook references

 * , Page 82, Chapter 2, Section 13 (the term Sorgenfrey line is not used, and the line is simply alluded to as the real numbers with the lower limit topology)