1 Ocak 2017 Dergi makalesi Açık Erişim

Gillam, W. D.; Karan, A.

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    <subfield code="a">In 1914, F. Hausdorff defined a metric on the set of closed subsets of a metric space X. This metric induces a topology on the set H of compact subsets of X, called the Hausdorff topology. We show that the topological space H represents the functor on the category of sequential topological spaces taking T to the set of closed subspaces Z of T x X for which the projection pi(1) : Z -&amp;gt; T is open and proper. In particular, the Hausdorff topology on H depends on the metric space X only through the underlying topological space of X. The Hausdorff space H provides an analog of the Hilbert scheme in topology. As an example application, we explore a certain quotient construction, called the Hausdorff quotient, which is the analog of the Hilbert quotient in algebraic geometry. (C) 2017 Elsevier B.V. All rights reserved.</subfield>
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    <subfield code="a">The Hausdorff topology as a moduli space</subfield>
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