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Analysis, Topology and Applications 2008 (ATA2008)
May 30 - June 4, 2008
Technical Faculty, Cacak, University of Kragujevac
Vrnjacka Banja, Serbia, Serbia

Organizers
Dragan Djurcic, Ljubisa D.R. Kocinac, Malisa R. Zizovic

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A general solution of the Birkhoff's problem 81
by
Antonio Pulgarín
Dept. of Math. Univ. of Extremadura, Cáceres (Spain)
Coauthors: Miroslav Hušek

The famous Birkhoff's problem 81 can be stated as follows: Which lattice-theoretic conditions are required for a lattice L to be isomorphic to the lattice C(X) of real continuous functions on a compact Hausdorff space X?. Anderson-Blair gave in 1961 an answer to this problem by using among others conditions that every continuous ideal of a characterizing sublattice L of C(X) has a least upper bound in L. We provide a lattice characterization of C(X) for X a completely regular space.

Date received: April 29, 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 # cawq-10.