On \sigma-discrete, T-finite and Tree-type Topologies
by
Ulrich Heckmanns
Mathematisches Institut der Universität München, Germany
Coauthors: Ulrich Heckmanns (Department of Mathematics and Statistics, York University, Canada)

A regular space is T-finite if and only if it is hereditarily strongly collectionwise Hausdorff and \sigma-pseudo-closed discrete. Every finer regular topology on such a space is hereditarily ultraparacompact. \sigma-pseudo-closed discreteness is strictly between \sigma-closed discreteness and \sigma-discreteness. Every T-finite, regular topology is finer than a (more or less) canonical topology defined on a tree of height <= \omega. These tree-type topologies (for arbitrary height) are always ultraparacompact and monotonically normal. A space is non-Archimedean and left separated if and only if it is a lob and of tree-type. Using the notion of T-finiteness, it is easy to show that the ring of polynomials over an arbitrary field, endowed with the ideal topology, is hereditarily ultraparacompact.

Date received: June 27, 1997

Copyright © 1997 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 # caao-28.