A new look at Counterexamples in topology

The book Counterexamples in Topology is a useful catalogue of topological spaces and properties. This thesis extends that catalogue to the properties of sobriety and packedness, and describes some related theory. A purely topological account of sobriety and sober reflections is given, together with an account of the connection with point-free topology which motivates it. Concrete constructions of the sober, T0 and T1 reflections of a topological space are given, and these are calculated for each space in Counterexamples in Topology. These are used to study the relationship between sobriety and the T1 separation property. The notion of a specialization topology is introduced as a means of constructing topological spaces from quasiordered sets. The Alexandrov, Scott and weak topologies are described and shown to be examples of this notion. The sobriety and sober reflections of specialization topologies are considered, and these motivate a suggestion for a generalization of the notion of a topological space. The calculations in this thesis are summarized in two reference tables.

Name dc:type.qualificationname

other

Level dc:type.qualificationlevel

masters

Year dc:date.issued

2002

Author dc:creator

• Kirby, J

Language dc:language

en