A circle is not the generalized inverse limit of a subset of [0,1]²

Illanes, Alejandro

doi:10.1090/S0002-9939-2011-10876-1

A circle is not the generalized inverse limit of a subset of $[0,1]^{2}$
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by Alejandro Illanes PDF

Proc. Amer. Math. Soc. 139 (2011), 2987-2993 Request permission

Abstract:

In this paper we show that the simple closed curve cannot be obtained as the inverse limit of an upper semi-continuous multivalued function from $[0,1]$ into $[0,1]$.

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