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cmr10AbstractStonedualityisaradicalreformulationofgeneraltopGology*,)_inwhichthetopGology onaspace
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wemayalsousecontinuousfunctionsbGetweenthespaces^Y Tand^X$.LInthetraditionalformulation,theseLspacescarrytheScotttopGology*,and\Scott-continuous"LfunctionsarethosebGetween|theinnitarylatticesthatpreservedirectedjoins.AllframehomomorphismsareScott-continuous,~butCbScott-continuousfunctionsingeneralneednotpreservenitemeetsandjoins.Continuous֚functionsbGetween֚thespacesthattheframesr}'epresentrin֚localetheorycorrespond,ofUUcourse,toframehomomorphismsintheoppGositedirection. ThegeneralplanfortranslatingatheoremoftopGologyintoabstractStonedualityisthereforeto!massagetheloGcalicformulationinsuchawaythatonlyScott-continuousfunctionsbGetweenframesareused. Inparticular,