More on Co-existentially Closed Continua
by
Paul Bankston
Marquette University

We are making slow but steady progress in solving the (dualized) analogy:

X is the class of co-existentially closed continua, well defined via ``abstract nonsense.'' Every member of X is of covering dimension one, and is indecomposable. Moreover, every metrizable continuum in X is hereditarily indecomposable; at least one is not arc-like. Any arc-like member of X must be a pseudo-arc. No easily specified examples, however, are yet known.

In essence we are trying to establish a ``Nullstellensatz'' for continuum theory. This may be an impossible goal, but at least the attempt gives us a fresh perspective on some familiar continuum-theoretic notions.

http://marque.mscs.mu.edu/Faculty/Bankston.html

Date received: January 13, 2000

Copyright © 2000 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 # cady-03.