On the topological structure of spaces of fuzzy compacta

  • Authors:

  • Lili Zhang;Jan J. Dijkstra

  • Affiliations:

  • Department of Mathematics and Physics, Xi'an Technological University, Xi'an, Shaanxi 710032, PR China;Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2011

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Abstract

We prove that the space of fuzzy compacta in a Peano continuum is homeomorphic to the Hilbert space @?^2. As a corollary we find that the spaces of fuzzy compacta in R^n and @?^2 are also homeomorphic to Hilbert space.