Sorgenfrey line

The Sorgenfrey line is a nonstandard topologyMathworldPlanetmath on the real line . Its topology is defined by the following base of half open intervalsPlanetmathPlanetmath


Another name is lower limit topology, since a sequence xα converges only if it converges in the standard topology and its limit is a limit from above (which, in this case, means that at most finitely many points of the sequence lie below the limit). For example, the sequence (1/n) converges to 0, while (-1/n) does not.

This topology is finer than the standard topology on . The Sorgenfrey line is first countable and separable, but is not second countable. It is therefore not metrizable.


Title Sorgenfrey line
Canonical name SorgenfreyLine
Date of creation 2013-03-22 13:03:45
Last modified on 2013-03-22 13:03:45
Owner yark (2760)
Last modified by yark (2760)
Numerical id 9
Author yark (2760)
Entry type Example
Classification msc 55-00
Classification msc 54-00
Classification msc 22-00
Synonym Sorgenfrey topology
Defines lower limit topology