Philipp Sünderhauf

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In recent years, there has been a considerable amount of work on using continuous domains in real analysis. Most notably are the development of the generalized Riemann integral with applications in fractal geometry, several extensions of the programming language PCF with a real number data type, and a framework and an implementation of a package for exact(More)
Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets. The usual criterion to check sobriety involves either irreducible closed subsets or completely prime lters of open sets. This paper provides an alternative possibility, thus trying to make sobriety easier to(More)
If a posets lacks joins of directed subsets, one can pass to its ideal completion. But doing this means also changing the setting: The universal property of ideal completion of posets suggests that it should be regarded as a functor from the category of posets with monotone maps to the category of dcpos with Scott-continuous functions as morphisms. The same(More)
We investigate the representation of real numbers by sequences of digits, thought of as radix expansions. “Faithful” refers to the fact that we overcome the classical problem of multiple representations for certain numbers. This is established by employing a suitable quasi-uniform structure on the set of finite sequences. (The paper contains a motivating(More)
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