Monotone and/or open homogeneity
by
Carl R. Seaquist
Texas Tech University

In this talk we summarize some of the recent results regarding homogeneity with respect to maps that are either open, monotone, or both. A space X is homogeneous with respect to a class of functions if and only if for every two points x and y in X there exists a continuous function from X onto X that is in the class and that takes x to y. We will describe results that show that the disk is open homogeneous but not monotone homogeneous, that show the Sierpi\'nski plane universal curve is monotone open homogeneous, and that show that there are many other Peano continua that are not homogeneous but are monotone open homogeneous.

Date received: February 18, 1997

Copyright © 1997 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 # caak-52.