Concrete sheaves and continuous spaces

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buir.advisorÜnlü, Özgün
dc.contributor.authorÖzkan Recep
dc.date.accessioned2016-07-01T11:11:48Z
dc.date.available2016-07-01T11:11:48Z
dc.date.issued2015
dc.departmentDepartment of Mathematicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.description.abstractIn algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous spaces which is more general than the concept of topological manifolds but more specific when compared to topological spaces. After that, it will be shown that the category of continuous spaces have ”convenient” properties we seek. For this, we first define concrete sites, concrete sheaves and say that a generalized space is a concrete sheaf over a given concrete site. Then it will be proved that a category of generalized spaces (for a given concrete site) has all limits and colimits. At the end, it will be proved that the category of continuous spaces is actually equivalent to the category of generalized spaces for a specific concrete site.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityÖzkan Recepen_US
dc.format.extentvii, 33 leavesen_US
dc.identifier.itemidB151174
dc.identifier.urihttp://hdl.handle.net/11693/30074
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSite and Sheavesen_US
dc.subjectGeneralized spacesen_US
dc.subject.lccB151174en_US
dc.titleConcrete sheaves and continuous spacesen_US
dc.typeThesisen_US

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