The space of Lelek fans in the Cantor fan is homeomorphic to Hilbert space
Jan J. DIJKSTRA and Lili ZHANG
Source: J. Math. Soc. Japan Volume 62, Number 3
(2010), 935-948.
Abstract
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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Keywords: strongly discontinuous functions; upper semicontinuous functions; Lelek fan; Cantor fan; hypograph metric; Hilbert space; pseudointerior of the Hilbert cube
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1280496824
Digital Object Identifier: doi:10.2969/jmsj/06230935
Zentralblatt MATH identifier: 05786475
Mathematical Reviews number (MathSciNet): MR2648067
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