Abstract
Suppose that for each i≥0, Ii=[0,1] and f is an inverse sequence of upper semicontinuous surjective functions fi+1:Ii+1→2Ii, each with a path-connected graph. We investigate necessary and sufficient conditions for lim←f to be path-connected. We define the notion of a path-component base and show that if f admits a path-component base then lim←f is not path-connected, and we give a characterisation of path-connected Mahavier products of f.
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