Baire spaces and the Wijsman topology

Cao, J
Tomita, A
Item type
Conference Contribution
Degree name
Journal Title
Journal ISSN
Volume Title
AUT University

In 1960s, when he studied Banach space geometry, R. Wijsman considered the weak topology on the collection of nonempty closed subsets of a metric space generated by the distance functionals viewed as functions of set argument. Nowadays, this topology is known as the Wijsman topology. Since then, there has been a considerable effort in exploring various completeness properties of this type of hyperspaces. For example, C. Constantini showed that the Wijsman hyperspace of a Polish space is Polish, and there exists a complete metric space whose Wijsman hyperspace fails to be Cech-complete. Motivated by these facts, it makes sense for us to investigate the Baireness of Wijsman hyperspaces. In this talk, I shall present some recent progress in this direction. In particular, I shall show that the Wijsman hyerspace of a metric hereditarily Baire space must be Baire. This result settles a problem posed by L. Zsilniszky at the 10th Prague Toposym in 2006.

International Conference on Topology and its Applications, December 3-7, 2007
Rights statement
NOTICE: this is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in (see Citation). The original publication is available at (see Publisher's Version)