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A generalization of the construction of containing spaces
by
S. D. Iliadis
University of Patras, Patras, Greece
We give a method of construction of containing spaces, which is a generalization of that given in [1]. In particular, we have the following result.
Let \nu and \tau be infinite cardinals such that:
(\alpha) |P\nu(\tau)| <= \tau, and
(\beta) |P(P(\pi))| <= \tau for every cardinal \pi less than \nu.
(For every set X, by P\nu(X) we denote the set of all subsets of X of cardinality < \nu and by P(X) the set of all subsets of X). Then, in the class of all (regular) T0-spaces of weight <= \tau with the property that the intersection of less than \nu many open subsets is open, there exists a universal element.
References
[1] S. D. Iliadis, A construction of containing spaces, To appear in Topology and its Applications.
Date received: June 23, 2000
Copyright © 2000 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 # caeh-37.