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- W2010904552 abstract "When computing on a (generally) uncountable topological structure gne; , such as the topological field of real numbers R, one must by necessity compute on a set of concrete approximations P for gne; . One way to do this is to represent the original structure gne; using P in such a way that computations on P transfer to approximate computations on gne; . Two such representations are considered, domain representability and representability by formal spaces , and these are compared for the class of locally compact regular spaces. It is shown that for locally compact regular spaces the two representations are equivalent over P for natural sets of approximations P . In addition it is shown that under rather general conditions, a continuous function between topological spaces represented by formal spaces over P 1 and P 2 , respectively, lifts to a continuous function between the corresponding domains, the ideal completions of p 1 and p 2 ." @default.
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- W2010904552 title "Representability of locally compact regular spaces by domains and formal spaces" @default.
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- W2010904552 doi "https://doi.org/10.1016/s0304-3975(96)00152-1" @default.
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