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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Note on the Constructible Sets of a Topological Space
by
Jean-Paul Allouche
CNRS, LMD

We study the so-called constructible sets: they are the sets in the Boolean algebra generated by the closed and open sets of a toplogical space. It is well known that these sets, which are used inter alia in Algebraic Geometry, are exactly the finite unions of locally closed sets, (a locally closed set being the intersection of a closed and of an open set).

We prove a seemingly not known characterization of these sets, that permits to give an algorithm to decide whether a given set is constructible. Furthermore this construction provides us with the smallest n for which a constructible set is the union of n locally closed sets.

Date received: April 12, 1996

Copyright © 1996 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 # caae-02.