1 Ocak 2017 Dergi makalesi Açık Erişim

Gillam, W. D.; Karan, A.

Citation Style Language JSON

{
  "DOI": "10.1016/j.topol.2017.10.003", 
  "abstract": "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 -> 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.", 
  "author": [
    {
      "family": "Gillam", 
      "given": " W. D."
    }, 
    {
      "family": "Karan", 
      "given": " A."
    }
  ], 
  "container_title": "TOPOLOGY AND ITS APPLICATIONS", 
  "id": "111146", 
  "issued": {
    "date-parts": [
      [
        2017, 
        1, 
        1
      ]
    ]
  }, 
  "page": "102-111", 
  "title": "The Hausdorff topology as a moduli space", 
  "type": "article-journal", 
  "volume": "232"
}