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The regularlocallycompact coreflection of stably locally compact locale
 Journal of Pure and Applied Algebra
, 2001
"... The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame. We show that the patch construction exhibits (i) the category of regular locally compact locales and perfect maps as a coreflective subcategory of the category of stably locally comp ..."
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Cited by 18 (9 self)
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The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame. We show that the patch construction exhibits (i) the category of regular locally compact locales and perfect maps as a coreflective subcategory of the category of stably locally compact locales and perfect maps,
Exponentiability Of Perfect Maps: Four Approaches
, 2002
"... Two proofs of the exponentiability of perfect maps are presented and compared to two other recent approaches. One of the proofs is an elementary approach including a direct construction of the exponentials. The other, implicit in the literature, uses internal locales in the topos of setvalued sh ..."
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Cited by 1 (1 self)
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Two proofs of the exponentiability of perfect maps are presented and compared to two other recent approaches. One of the proofs is an elementary approach including a direct construction of the exponentials. The other, implicit in the literature, uses internal locales in the topos of setvalued sheaves on a topological space.
Relative Compactness Conditions For Toposes
"... this paper a systematic study is made of various notions of "proper map" in the context of toposes. Modulo some separation conditions, a proper map Y ! X of spaces is generally understood to be a continuous function which preserves compactness of subspaces under inverse image, and which therefore in ..."
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this paper a systematic study is made of various notions of "proper map" in the context of toposes. Modulo some separation conditions, a proper map Y ! X of spaces is generally understood to be a continuous function which preserves compactness of subspaces under inverse image, and which therefore in particular has compact fibers. In this spirit, a first definition of proper map between toposes was put forward by Johnstone in []. There, a map of toposes f : F ! E was called proper if f
Semantic domains, injective spaces and monads (Extended Abstract)
"... Many categories of semantic domains can be considered from an ordertheoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. Whe ..."
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Many categories of semantic domains can be considered from an ordertheoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. When one embeds topological spaces into domains, one requires that the Scott continuous maps between the host domains fully capture the continuous maps between the guest topological spaces. This property of the host domains is known as injectivity. For example, the continuous Scott domains are characterized as the injective spaces over dense subspace embeddings (Dana Scott, 1972, 1980). From a third point of view, the continuous Scott domains arise as the algebras of a monad (Wyler, 1985). The topological characterization by injectivity turns out to follow from the algebraic characterization and general category theory (Escard'o 1998). In this paper we systematically consider monads that arise ...