Projective Topological Spaces and Injective Topological Algebras
by
Domenico Rosa
Teikyo Post University

For many subcategories of Hausdorff spaces, the P-projective spaces are precisely the extremally disconnected spaces, where P is the class of perfect onto maps. This talk will discuss Tychonoff spaces that are F-projective, where F consists of all maps f : X --> Y such that every compact subset of Y is the image of some compact subset of X. These maps are precisely those that induce embeddings C(f) : C(Y) --> C(X), with respect to the compact-open topology, between the corresponding function algebras. We show that a space is F-projective iff it is the disjoint topological union of extremally disconnected compact spaces. The corresponding function algebra is injective in a suitable subcategory of locally m -convex algebras.

Date received: April 12, 1996

Copyright © 1996 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 # caaf-69.