Intervals in the Lattice of Topologies
by
D. W. McIntyre
University of Auckland

The collection of all topologies on a given set X forms a lattice T under inclusion. Given \sigma, \tau in T one can form the interval

[\sigma, \tau] = { \mu in T : \sigma subset or equal \mu subset or equal \tau} .

We will discuss the problem of characterizing the lattices L such that we can find Hausdorff topologies \sigma and \tau such that [\sigma, \tau] is isomorphic to L.

For example, if L is finite then it is realizable as an interval only if it is distributive. However, some infinite non-distributive lattices can be realized as intervals.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-56.