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While I was talking to some colleagues, one of them said that there exists a topological space $X$ such that $X$ is uncountable, non-discrete and homeomorphic to $\mathscr{F}[X]$ (the Pixley-Roy hyperspace). Unfortunately, he can't remember where he read. The only thing he remembers is that this result appears in an article by Peter Niykos and E. V. Douwen or some article related to them. Anyone knows where I can find that reference? Or the name of the paper where that result appears?

Thanks in advance!

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    $\begingroup$ I found one review on mathscinet that mentions a positive result $\endgroup$
    – KP Hart
    Nov 2 at 16:32

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