A Unified Theory of Scattered Metric Spaces
by
A. J. Jayanthan
Goa University
Coauthors: V. Kannan (University of Hyderabad)

We give a complete answer to the following questions:

(i) What are all the joins of scattered metric topologies?

(ii) What are all the complete metric spaces, every finer regular topology on which has dimension zero (normal, paracompact etc.)?

The answers are obtained by first proving the following theorem:

Let P be a property that is invariant under sums and sequential sums and let the singleton space satisfy P. Then every scattered metric space satisfies P.

This is a unifying theorem for which many important theorems originally proved by Stone, Katetov, Sierpi\'nski etc. become corollaries. This also yield many new results, for instance (i) and (ii).

Financially supported by the Council of Scientific and Industrial Research, India

Date received: June 24, 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 Mathematical Conference Abstracts. Document # caah-45.