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dc.contributor Graduate Program in Mathematics.
dc.contributor.advisor Gillam, William Daniel.
dc.contributor.author Karan, Alperen.
dc.date.accessioned 2023-03-16T11:21:41Z
dc.date.available 2023-03-16T11:21:41Z
dc.date.issued 2015.
dc.identifier.other MATH 2015 K37
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/15281
dc.description.abstract In 1914, Felix Hausdor introduced a metric, called the Hausdor metric on the set of closed subspaces, Hausdor space, of a metric space. This metric and the corresponding topology are the main objects of the study. In algebraic geometry, there is an analogous object called the Hilbert scheme, whose points correspond to closed subschemes of a projective variety X. We give a modular interpretation of the Hausdor space analogous to the one for the Hilbert scheme. The Hilbert scheme is used in various structures in algebraic geometry; using the Hausdor space we can mimic these constructions in topology. For example, when an algebraic group acts on a projective variety, one can form a quotient X Hilb G called the Hilbert quotient. We consider the analogous Hausdor quotient X Haus G associated to a topological group acting on a metric space. We note that this quotient has some desirable properties: When X is compact X Haus G is compact and when G is also compact X Haus G is the usual quotient X{G. In addition to the Hausdor topology, one can also topologize the set of closed subspaces of X by considering the compact open topology on the set of continuous maps from X to the Sierpinski space. Although the resulting Hilbert space is less well-behaved than the Hausdor space, it admits a nice modular interpretation when X is locally compact.
dc.format.extent 30 cm.
dc.publisher Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015.
dc.subject.lcsh Topology.
dc.subject.lcsh Hilbert algebras.
dc.title Topologies on families of closed subsets
dc.format.pages vii, 46 leaves ;


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