Connectedness of inverse limits with set-valued functions
Keywords:
connected, inverse limits with set-valued functionsAbstract
We establish general results for determining connectedness of inverse limits on continua with set-valued bonding functions. These results generalize all theorems in the literature where connectedness of the inverse limit can be established by checking easily observable properties of the bonding functions. For inverse limits on $[0,1]$, we note several useful special cases of our main theorem. The results provide answers to two questions of W. T. Ingram. We give a number of examples to illustrate the utility of the results.
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