Monotone insertion of continuous functions between continuous ones
by
Chris Good
University of Birmingham
Coauthors: Ian Stares

Kubiak showed that the monotone version of the Katetov-Tong characterization of normality is, in fact, equivalent to monotone normality. Pan asked whether the monotone version of Dowker's theorem has a characterization in terms of known properties. We show that a space X is stratifiable if and only if for each upper semi-continuous g : X --> R and lower semi-continuous h : X --> R such that g <= h, there is a continuous f_{g, h} : X --> R such that g <= f_{g, h} <= h and such that f_{d, e} <= f_{g, h} whenever d <= g and e <= h.

We may briefly mention other possible monotonic versions of countable paracompactness.

Date received: July 30, 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 # caap-07.