Notes on injective spaces
by
Ales Pultr
Charles University, Prague, Czech Republic
Coauthors: Francesca Cagliari (Univ. Bologna, Italy)

It is a well-known fact that the injective objects in Top₀ are precisely the retracts of the powers S^M of the Sierpi\'nski space. Our notes concern the internal structure of such retracts, in particular the following:

By a well known result of D. Scott, the injective spaces can be viewed as continuous lattices. The structure of continuous maps r:S^M --> S^M such that r o r=r gives rise to a sort of ``inference systems" analogous to Scott's information systems, the relation of which to continuous lattices is parallel to that of information systems and domains.

Another topic to be discussed is the case of the retracts of S^M that are topologies on the set M.

Date received: March 13, 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 # cafw-64.