On topologies arising from the de Groot dual I
by
Martin Maria Kovar
Technical University of Brno

A topology \tau^d is said to be the de Groot dual of a topology \tau on a set X if \tau^d has a closed base which consists of all compact saturated sets in the topological space (X, \tau). The Problem 540 of J. Lawson and M. Mislove in Open Problems in Topology [LM] asks whether the process of iterating the de Groot dual terminates, after finitely many steps, by two topologies dual to each other, and which topologies can arise as duals. A general and positive answer to the first part of the question was given by the author in 2001 [Ko]. Now we will study some further properties of the de Groot dual, including the remaining unsolved part of Problem 540. A free continuation of the talk will be presented in the 2003 Summer Conference on Topology and its Applications in Washington.

References:

[Ko] Kovár, M. M., At most 4 topologies can arise from iterating the de Groot dual, Topology and its Applications, 130 (2003), 175-182

[LM] Lawson J.D., Mislove M., Problems in domain theory and topology, Open problems in topology, edited by van Mill J., Reed G. M., North-Holland, Amsterdam, 1990, 349-372

Date received: May 28, 2003