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Admissible representations of probability measures
 Electronic Notes in Theoretical Computer Science
"... In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We ..."
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Cited by 9 (0 self)
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In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. This canonical representation turns out to be admissible with respect to the weak topology on M(X). Moreover, we prove that for countably based topological spaces X the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology on M(X).
Representing Probability Measures using Probabilistic Processes
 Journal of Complexity
, 2006
"... In the Type2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as “names ” for the elements they represent. Given such a representation, we show that probabilistic processes on infinite words generate Borel probability measures on the repres ..."
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Cited by 7 (2 self)
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In the Type2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as “names ” for the elements they represent. Given such a representation, we show that probabilistic processes on infinite words generate Borel probability measures on the represented space. Conversely, for several wellbehaved types of space, every Borel probability measure is represented by a corresponding probabilistic process. Accordingly, we consider probabilistic processes as providing “probabilistic names ” for Borel probability measures. We show that integration is computable with respect to the induced representation of measures. 1
Two Preservation Results for Countable Products of Sequential Spaces
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
"... We prove two results about the sequential topology on countable products of sequential topological spaces. First, we show that a countable product of topological quotients yields a quotient map between the product spaces. Second, we show that the reflection from sequential spaces to its subcategory ..."
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Cited by 3 (3 self)
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We prove two results about the sequential topology on countable products of sequential topological spaces. First, we show that a countable product of topological quotients yields a quotient map between the product spaces. Second, we show that the reflection from sequential spaces to its subcategory of monotone ωconvergence spaces preserves countable products. These results are motivated by applications to the modelling of computation on nondiscrete spaces.
An Effective TietzeUrysohn Theorem for QCBSpaces
 Journal of Universal Computer Science, Vol
, 2009
"... Abstract: The TietzeUrysohn Theorem states that every continuous realvalued function defined on a closed subspace of a normal space can be extended to a continuous function on the whole space. We prove an effective version of this theorem in the Type Two Model of Effectivity (TTE). Moreover, we in ..."
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Abstract: The TietzeUrysohn Theorem states that every continuous realvalued function defined on a closed subspace of a normal space can be extended to a continuous function on the whole space. We prove an effective version of this theorem in the Type Two Model of Effectivity (TTE). Moreover, we introduce for qcbspaces a slightly weaker notion of normality than the classical one and show that this property suffices to establish an Extension Theorem for continuous functions defined on functionally closed subspaces. Qcbspaces are known to form an important subcategory of the category Top of topological spaces. QCB is cartesian closed in contrast to Top.
Stability of representations of effective partial algebras
, 2011
"... Key words Numberings, recursive equivalence, computable stability, effective partial algebras, computable ..."
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Key words Numberings, recursive equivalence, computable stability, effective partial algebras, computable
Under consideration for publication in Math. Struct. in Comp. Science Quotients of countably based spaces are not
, 2006
"... Dedicated to Klaus Keimel on the occasion of his 65th birthday In this note we show that quotients of countably based spaces (qcb spaces) and topological predomains as introduced by M. Schröder and A. Simpson are not closed under sobrification. As a consequence replete topological predomains need no ..."
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Dedicated to Klaus Keimel on the occasion of his 65th birthday In this note we show that quotients of countably based spaces (qcb spaces) and topological predomains as introduced by M. Schröder and A. Simpson are not closed under sobrification. As a consequence replete topological predomains need not be sober, i.e. in general repletion is not given by sobrification. Our counterexample also shows that a certain tentative “equalizer construction ” of repletion fails for qcb spaces. Our results extend also to the more general class of core compactly generated spaces.