Overview

Though the search for good selectors dates back to the early 20th century, selectors play an important role in contemporary research. This book assembles the literature into a presentation of what is known and proven about selectors - and what remains to be found. The authors focus on selection theorems that are related to the axiom of choice, particularly selectors of small Borel or Baire classes. After examining some of the relevant work of Michael and Kuratowski and Ryll-Nardzewski and presenting background material, the text constructs selectors obtained as limits of functions that are constant on the sets of certain partitions of metric spaces. These include selection theorems for maximum monotone maps, for the subdifferential of a continous convex function, and for some geometrically defined maps, namely attainment and nearest-point maps.

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9780691096285

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John E. Jayne, PhD, DSc, is Professor of Mathematics at University College London and has been President of the International Mathematics Competition for university students since its inception in 1994. C. Ambrose Rogers, DSc, FRS, is Professor Emeritus at University College London, where he was Astor Professor of Mathematics for almost thirty years. He is an Elected Fellow of the Royal Society and a former President of the London Mathematical Society. His many awards and honors include the Junior Berwick Prize and De Morgan Medal of the London Mathematical Society.

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