Continua which are S4-spaces in the sense of Michael
by
Francis Jordan
Loyola University New Orleans

We show that every S4-continuum is a dendrite (hereditarily decomposable Peano continuum). Recall that a continuum X is S4 provided that for any partition D of X into compact sets there is a continuous map f:D --> X such that f(d) is an element d for all d in D.

The proof of the result involves the transfinite construction of non-continuous bijections with connected graphs. Along the way, we also prove a selection result for montone maps with nowhere dense point inverses of continua onto the arc.

Date received: February 5, 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-33.