A Compendium of Continuous Lattices - Hardcover

Gierz, G.; Hofmann, K. H.; Keimel, Klaus; Mislove, M.; Scott, D. S.

Hardcover

ISBN 10: 354010111X ISBN 13: 9783540101116

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1980

Synopsis

A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1980
• Language: English
• ISBN 10: 354010111X
• ISBN 13: 9783540101116
• Binding: Hardcover
• Number of pages: 371