Special Resolutions and their Properties.
by
Brian van Dam
University of Auckland

In this talk, we will examine the concept of special resolutions, a technique used to generate new spaces from old. It can be thought of as taking a space, and magnifying each point up into a space of its own.

The structure of a resolved space will be investigated, including the ideas of germs and embedding sets. Germs allow us to generalise resolutions by using partial multifunctions, and embedding sets `bind' the resolved space together making certain connectivity results possible, for example.

The parallel nature of the resolution theory, dependant on whether upper semi-continuous or lower semi-continuous multifunctions are used in resolving, is illustrated with a few examples.

Date received: June 7, 1999

Copyright © 1999 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 # cacl-64.