Atlas home || Conferences | Abstracts | about Atlas

Spring Topology and Dynamics Conference 2006
March 23-25, 2006
University of North Carolina at Greensboro
Greensboro, NC, USA

Organizers
Gregory Bell, Alexander Chigogidze, Paul Duvall, Jan Rychtar, Jerry Vaughan

View Abstracts
Conference Homepage

Function Spaces over Generalized Ordered Topological Spaces
by
Raushan Buzyakova
Brooklyn College

We describe the structure of spaces of continuous step functions over GO-spaces. We establish a relation between the Dedekind completion of a GO-space L and algebraic and topological properties of the space of continuous functions from L to 2 with finitely many steps. We use the established relation to prove that a countably compact GO-space L has Lindelöf Cp iff the Dedekind remainder of L is Lindelöf and every compact subspace of L is metrizable. Or equivalently, a countably compact GO-space L has Lindelöf Cp iff every compact subspace of L is metrizable and a Gd-set in L. Other results regarding Cp over GO-spaces are obtained.

Date received: February 25, 2006

Copyright © 2006 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 # caqs-88.