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Topological and Limitspace subcategories of Countablybased Equilogical Spaces
, 2001
"... this paper we show that the two approaches are equivalent for a ..."
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Cited by 22 (4 self)
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this paper we show that the two approaches are equivalent for a
Continuous Functionals of Dependent Types and Equilogical Spaces
, 2000
"... . We show that dependent sums and dependent products of continuous parametrizations on domains with dense, codense, and natural totalities agree with dependent sums and dependent products in equilogical spaces, and thus also in the realizability topos RT(P!). Keywords: continuous functionals, depen ..."
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Cited by 12 (8 self)
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. We show that dependent sums and dependent products of continuous parametrizations on domains with dense, codense, and natural totalities agree with dependent sums and dependent products in equilogical spaces, and thus also in the realizability topos RT(P!). Keywords: continuous functionals, dependent type theory, domain theory, equilogical spaces. 1 Introduction Recently there has been a lot of interest in understanding notions of totality for domains [3, 23, 4, 18, 21]. There are several reasons for this. Totality is the semantic analogue of termination, and one is naturally interested in understanding not only termination properties of programs but also how notions of program equivalence depend on assumptions regarding termination [21]. Another reason for studying totality on domains is to obtain generalizations of the nitetype hierarchy of total continuous functionals by Kleene and Kreisel [11], see [8] and [19] for good accounts of this subject. Ershov [7] showed how the Klee...
A NonTopological View of Dcpo’s as Convergence Spaces. In
 Schellekens and A.K. Seda (Eds.), Proceedings of the First Irish Conference on the Mathematical Foundations of Computer Science and Information Technology
, 2003
"... ..."
The Largest Topological Subcategory of Countablybased Equilogical Spaces
, 1998
"... There are two main approaches to obtaining "topological" cartesianclosed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed  for example, the category of sequential spaces. Under the other, one generalises the notion of s ..."
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Cited by 4 (1 self)
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There are two main approaches to obtaining "topological" cartesianclosed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed  for example, the category of sequential spaces. Under the other, one generalises the notion of space  for example, to Scott's notion of equilogical space. In this paper we show that the two approaches are equivalent for a large class of objects. We first observe that the category of countablybased equilogical spaces has, in a precisely defined sense, a largest full subcategory that can be simultaneously viewed as a full subcategory of topological spaces. This category consists of certain "!projecting" topological quotients of countablybased topological spaces, and contains, in particular, all countablybased spaces. We show that this category is cartesian closed with its structure inherited, on the one hand, from the category of sequential spaces, and, on the other, from the cate...