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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Please, be discreet .... don't judge a space from its cover by discretes!
by
Santi Spadaro
Auburn University

We study the cardinal inequality dis(X) ≥ D(X) on generalized metric spaces, where dis(X) is the least cardinality of a cover of X by relatively discrete sets and D(X) is the least cardinality of a non-empty open set in X.

In particular, we prove that dis(X) ≥ D(X) holds for

  1. Paracompact Baire s-spaces.

  2. Collectionwise Hausdorff Baire developable spaces.

We show examples of well-mannered spaces for which the above inequality fails: for example, we construct a Normal Baire Moore space X for which dis(X) < D(X).

Date received: February 4, 2008

Copyright © 2008 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 # cawk-34.