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Nordic Conference on Topology and its Applications (NORDTOP2001)
August 7-9, 2001
Sophus Lie Conference Centre
Nordfjordeid, Norway

Organizers
Peter Collins, Bjoern Jahren, Dusan Repovs, Stephen Watson

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Selections and order-like relations
by
Tsugunori Nogura
Ehime University (Matsuyama, Japan)
Coauthors: Valentin Gutev(University of Natal, Durban, South Africa)

Every selection f for the family F(X) of at most two-point subsets of a set X naturally defines an order-like relation \preceqf on X by x \preceq y if and only if f({x, y})=x. In the present talk we study the relationship between \preceqf and the possibile topologies T on X which realize the continuity of f with respect to the Vietoris topology on F2 generated by T. We also study a similar problem about selections for the Vietoris hyperspace of all non-empty closed subsets of a Hausdorff apace (X, T).

Date received: May 31, 2001

Copyright © 2001 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 # cagf-08.