Means on continua
by
Alejandro Illanes
Universidad Nacional Autonoma de Mexico

Let X be a metric continuum. A mean on X is a continuous function m from the product X ×X into X such that m(x, x) = x and m(x, y) = m(y, x) for every x, y in X. Answering a question by J. J. Charatonik we have proved that the Buckethandle continuum admits no mean. It is an open question if the arc is the only chainable continuum that admits a mean. We will talk about this and some related problems.

Date received: February 9, 2001

Copyright © 2001 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 # cagh-72.