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Colloquium on Topology, Gyula, Hungary
August 9-15, 1998
János Bolyai Mathematical Society
Budapest, Hungary

Organizers
M. Bognár, A. Császár (chairman), J. Gerlits, I. Juhász, E. Makai, G. Moussong, R. Rimányi, L. Soukup, A. Stipsicz, J. Szenthe, A. Szücs (secretary)

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Saturated Classes of Subsets and Universality
by
S. D. Iliadis
University of Patras

All spaces are assumed to be T0-spaces of weight less than or equal to a given infinite cardinal \tau. By a class of subsets we mean a class consisting of ordered pairs (Q, X), where Q is a subset of a space. An element (QT, T) of a class P of subsets is said to be universal (respectively, properly universal) if for every (QX, X) in P there exists an embedding i of X into T such that i(QX) subset QT (respectively, i-1(QT)=QX). Using a construction of containing spaces we will give the notion of a (complete) saturated class of subsets. In such a class there exists (properly) universal elements. However, saturated classes have ßomething more" than the existence of universal elements. For example, the intersection of saturated classes is also saturated, while the intersection of classes having universal elements may have no universal element. We will give some concrete (complete) saturated classes of subsets.

Date received: May 8, 1998

Copyright © 1998 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 # cabc-09.