Wijsman convergence: topological properties and embeddings
Files
Date
Authors
Supervisor
Item type
Conference Contribution
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
AUT University
Abstract
In 1966, R. A. Wijsman studied some optimum properties of the sequential probability ratio test, he considered a mode of convergence for sequences of closed convex sets in R^n. Since then, this type of convergence has attracted the attention of both analysts and topilogists, and its applications in convex analysis and Banach space geometry have been explored. Despite of investigation on Wijsman convergence in the past 40 years, some fundamental questions concerning its topology remain unsolved. For example, when does the Wijsman topology have the Baire property? When is the Wijsman topology normal? To attack these questions, the techniques of splitting and embedding have been employed. In this talk, I shall highlight recent progress towards these questions. In particular, some partial solutions and my recent joint work with H. J. K. Junnila , A. H. Tomita et al will be presented.Description
Keywords
Source
International Conference Japan-Mexico on Topology and its Applications, Colima, Mexico, September 27 - October 1, 2010
DOI
Publisher's version
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)