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A survey of the representations of categoriesChiu, Wing-kin. January 1967 (has links)
Thesis (M.A.)--University of Hong Kong, 1967. / Also available in print.
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Unifying the Baire category theoremHuber, George Michael January 1970 (has links)
The formulation of the Baire category theorem found in most elementary topology texts deals with two distinct classes of spaces: locally compact spaces, and complete metric spaces. This "dual theorem" status of Baire's theorem suggests the problem of finding one class of topological spaces for which the Baire category theorem can be proved and which includes both the locally compact spaces and the complete metric spaces. This thesis surveys and compares the three approaches to this problem taken by three methamticians.
The classical results of E. Čech achieve a unified Baire theorem by a Aefinl.ti.on of completeness different from that in current common usage. Johannes de Groot introduced a notion of subcompactness, generalizing compactness. K. Kunugi worked in the setting of complete ranked spaces which generalize uniform spaces and eliminate the need to assume regular separation in the space. This last point is the basis for the construction of a complete ranked space which is neither subcompact nor complete in the sense of Čech. It is also shown in the paper that there exist spaces subcompact but not complete in the sense of Čech, and that in certain special cases completeness in the sense of Čech implies subcompactness. / Science, Faculty of / Mathematics, Department of / Graduate
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Internal category theoryMelkonian, Sam January 1977 (has links)
No description available.
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Full embeddings and the category of graphsMendelsohn, Eric. January 1968 (has links)
No description available.
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Absoluteness properties in category theoryParé, Robert. January 1969 (has links)
No description available.
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Relations in categories.Meisen, Jeanne January 1972 (has links)
No description available.
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Completion of categories under certain limitsMeyer, Carol V. (Carol Vincent) January 1983 (has links)
No description available.
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Reflective subcategoriesBaron, Stephen. January 1967 (has links)
No description available.
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Neighbourhood operators on CategoriesRazafindrakoto, Ando Desire 03 1900 (has links)
Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: While the notions of open and closed subsets in a topological space are dual to each
other, they take on another meaning when points and complements are no longer
available. Closure operators have been extensively used to study topological notions
on categories. Though this has recovered a fair amount of topological results and has
brought an economy of e ort and insight into Topology, it is thought that certain
properties, such as convergence, are naturally associated with neighbourhoods. On
the other hand, it is interesting enough to investigate certain notions, such as that
of closed maps, which in turn are naturally associated with closure by means of
neighbourhoods.
We propose in this thesis a set of axioms for neighbourhoods and test them with
the properties of connectedness and compactness. / AFRIKAANSE OPSOMMING: Al is die twee konsepte van oop en geslote subversamelings in 'n topologiese ruimte
teenoorgesteldes van mekaar, verander hul betekenis wanneer punte en komplemente
nie meer ter sprake is nie. Die gebruik van afsluitingsoperatore is alreeds
omvattend in die studie van topologiese konsepte in kategorieë, toegepas. Alhoewel
'n redelike aantal topologiese resultate, groeiende belangstelling en groter insig tot
Topologie die gevolg was, word daar geglo dat seker eienskappe, soos konvergensie,
op 'n natuurlike wyse aan omgewings verwant is. Nietemin is dit van belang om
sekere eienskappe, soos geslote afbeeldings, wat natuurlik verwant is aan afsluiting,
te bestudeer.
In hierdie proefskrif stel ons 'n aantal aksiomas oor omgewings voor en toets dit
gevolglik met die eienskappe van samehangendheid en kompaktheid.
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Homology theories on the maping category /Elwin, John David. January 1970 (has links)
Thesis (Ph. D.)--Oregon State University, 1970. / Typescript (photocopy). Includes bibliographical references (leaf 49). Also available on the World Wide Web.
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