Continuous Decompositions
by
Carl R. Seaquist
Texas Tech University

In this talk we discuss a technique for building continuous decompositions that grew out of the work of R. D. Anderson in the early 1950s. We apply this technique to address several problems in continuum theory. In particular we will construct monotone open maps on various plane continua including the disk and the Sierpi\'nski curve. These maps will demonstrate that the disk is homogeneous with respect to open maps and that the Sierpi\'nski curve is homogeneous with respect monotone open maps. A space is homogeneous with respect to a class of functions if and only if for every two points in the space there exists a map from the space onto itself in the class of functions that takes the first point onto the second. Finally, we show that there are many other Peano continua that are not homogeneous but are homogeneous with respect to monotone open maps.

Date received: February 16, 1998

Copyright © 1998 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 # caas-87.