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A Compendium of Continuous Lattices (Paperback, Softcover reprint of the original 1st ed. 1980)
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A Compendium of Continuous Lattices (Paperback, Softcover reprint of the original 1st ed. 1980)
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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.
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