Cardinality of transitive sets of functions of the Cantor set
by
B. J. van der Steeg
T.U.Delft
Coauthors: K.P. Hart (T.U.Delft)

We investigate the minimal cardinality of transitive sets of functions of the Cantor set.

Here a transitive set of functions of a space X is a set of continuous self maps such that for every two elements x and y in X there exists a function in this set that maps x onto y or y onto x.

We will see that the continuum is less than or equal to the successor of the minimal cardinality of a transitive set for the Cantor set, and that it is consistent with ZFC that it is strictly less.

Date received: June 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 Conferences Inc. Document # caeu-19.