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  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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The Wijsman Convergence

Cao, J
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ICAA2010.pdf (1.242Mb)
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http://hdl.handle.net/10292/3539
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Abstract
In 1960's, when he studied some optimum properties of sequential probability ratio test, R. A. Wijsman considered a mode of convergence for sequences of closed sets such that if a sequence of proper lower semicontinuous convex functions defined on R^n (as associated with their epigraphs) converged, then the same could be said for the induced sequence of conjugate functions. In recognition of his contribution, this mode of convergence is now called the Wijsman convergence. Of course, the Wijsman convergence is topological, and the associated topology is called the Wijsman topology. In the past 40 years, there has been a considerable effort in extending Wijsman's results in infinite-dimensional Banach spaces, and exploring some properties of the Wijsman topology. It turns out that the Wijsman convergence and its topology have played important roles in the Banach Space Theory and Set-Valued Analysis. In this talk, I shall give an overview of the recent developments on the Wijsman topology. In particular, I shall discuss the Polishness, Baireness, the Amsterdam and other properties of this topology. Parts of my recent work with H Junnila and A Tomita will be presented, and some open questions in this area will be posed.
Date
January 24, 2010
Source
International Conference on Analysis and Applications, January 24-26, 2010
Item Type
Conference Contribution
Publisher
AUT University
Publisher's Version
http://www.squ.edu.om/Portals/87/Conference/ICAA10/Conference2010/ICAA10.html
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)

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