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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

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Quotient spaces and D-spaces
by
Dennis Burke
Miami University

We discuss the question of when quotient images of metric spaces are D-spaces.

Theorem. Any symmetrizable space X is a D-space (hereditarily).

Hence, quotient mappings, with compact fibers, from metric spaces have a D-space image. What about quotient s-mappings? Open images of metric spaces need not be D-spaces since w1 (being first-countable) is the open image of a metric space (even a s-discrete metric space). Arhangel'skii and Buzyakova have shown that spaces with a point-countable base are D-spaces so open s-images of metrics spaces are D-spaces.

Date received: February 28, 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 # cast-26.