Co-Connected Spaces

∗ Financial support of the Grant Agency of the Czech Republic under the grant no 201/96/0119 and of the Grant Agency of the Charles University under the grant GAUK 149 is gratefully acknowledged.

Co-connected spaces, i.e. the spaces X for which any continuous map X^2 → X factors through a projection, are investigated. The main result: every free monoid is isomorphic to the monoid of all nonconstant continuous selfmaps of a metrizable co-connected space.