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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 28 (4 self)
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this paper we show that the two approaches are equivalent for a
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 n ..."
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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...