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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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Closed Discrete Subspaces in First Countable Spaces
by
Kerry Smith
Franklin College of Indiana
Coauthors: Dennis Burke, Miami University

In this note, we consider the following three topological statements:

(1) NS: In every normal first countable space, closed discrete subspaces are separated.

(2) CPS: In every countably paracompact first countable T2 space, closed discrete subspaces are separated.

(3) CMGD: In every countably metacompact first countable T1 space, closed discrete subspaces are Gd-sets.

We construct general combinatorial statements that are equivalent, respectively, to each of the topological statements above. We then use the combinatorics to prove a chain of implications between the topological statements. We finish by asking if any of the implications can be reversed.

Date received: February 22, 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-69.