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Spring Topology and Dynamical Systems Conference
March 15-17, 2001
Centro de Convenciones
Morelia City, Michoacán, Mexico

Organizers
Alejandro Illanes, Sergio Macías, Jesus Muciño, María Luisa Pérez

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Developability of hyperspaces
by
László Zsilinszky
UNC Pembroke, USA
Coauthors: Lubica Holá (Institute of Mathematics, Academy of Sciences, Slovakia), Jan Pelant (Mathematical Institute, Academy of Sciences, Czech Republic)

Developability of the hyperspace (K(X), \tauV) of the nonempty compact subspaces of a Hausdorff base space X endowed with the Vietoris topology was established by Mizokami, who showed that K(X) is developable iff X is. Our results focus on characterizing developability and other properties (e.g. submetrizability, having a G\delta-diagonal, resp.) of hyperspace topologies on CL(X), the nonempty closed subsets of X. These topologies include the (bounded) Vietoris, Fell and locally finite topology. The main results demonstrate that the above hyperspaces are developable iff they are metrizable; a similar relationship exists between submetrizability and having a G\delta-diagonal. Possible generalizations of these results are discussed.

Date received: February 7, 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 # cagh-44.