The natural topology of the real line is generated by taking as a base the open intervals. Taking as a base the right half open intervals one obtains the Sorgenfrey topology (1947). It has a number of unusual properties which makes it a standard counter example in general topology. We construct a big variety of new topologies on the real line similar to Sorgenfrey’s and with additional extremal properties. In particular, in all of them there are closed discrete subsets of cardinality continuum.
DR. YEVHEN ZELENYUK
UNIVERSITY OF THE WITWATERSRAND,
Johannesburg, South Africa
Lecture 1: Classical topologies on the real line, 11:00 a.m.
Lecture 2: Some new topologies on the real line, 12:00 m.
