The space of Lelek fans in the Cantor fan is homeomorphic to Hilbert space

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  • Dijkstra Jan J.
    Faculteit der Exacte Wetenschappen, Afdeling Wiskunde, Vrije Universiteit Amsterdam
  • Zhang Lili
    Department of Mathematics and Physics, Xi'an Technological University

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We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous.

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