Journal ArticleDOI
Cartesian closed coreflective hulls
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In this article, conditions are established under which a given class of objects in a topological category will have a Cartesian closed coreflective hull, and the main theorem is used to discover new Cartesian-closed topological categories and to unify a diversity of known special results.Abstract:
Conditions are established under which a given class of objects in a topological category will have a Cartesian closed coreflective hull. The main theorem is used to discover new Cartesian closed topological categories and to unify a diversity of known special results. It also provides a mild criterion for the existence of Cartesian closed topological hulls.read more
Citations
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Topological improvements of categories of structured sets
TL;DR: In this paper, the authors discuss the properties of topological hulls and provide several illuminating examples, including concrete quasitopos hull and Wyler completion, for structured sets.
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General function spaces, products and continuous lattices
TL;DR: The compact-open topology for function spaces is usually attributed to R. H. Fox in 1945 as mentioned in this paper, but there is no earlier publication to attribute it to. But it is clear from Fox's paper that the idea of the compact-Open topology and its notable success in locally compact spaces were already familiar.
Journal ArticleDOI
Monoidal closed, Cartesian closed and convenient categories of topological spaces
Peter I. Booth,J. Tillotson +1 more
TL;DR: In this article, a unified theory of function spaces Mj^(Y, Z) with set-open topologies was developed, the sets in question being the continuous images of selected classes of topological spaces.
Journal ArticleDOI
Some open categorical problems in Top
Horst Herrlich,Miroslav Hušek +1 more
TL;DR: This paper discusses several open problems in categorical topology that deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.
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Powers and exponential objects in initially structured categories and applications to categories of limit spaces
TL;DR: In this paper, it is shown that reduction to finally and initially dense classes is possible for epireflective subcategories of the category of limit spaces containing a finite non-indiscrete space.
References
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Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
Journal ArticleDOI
Cartesian closed topological hulls
Horst Herrlich,L. D. Nel +1 more
TL;DR: In this article, it is shown that if a concrete category 9 admits embedding as a full finitely productive subcategory of a cartesian closed topological (CCT) category, then W admits such embedding into a smallest CCT category, its CCT hull.