Concerning continuous selections

Nadler, Sam B.; Ward, L. E.

doi:10.1090/S0002-9939-1970-0256360-9

Concerning continuous selections
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by Sam B. Nadler and L. E. Ward

Proc. Amer. Math. Soc. 25 (1970), 369-374

DOI: https://doi.org/10.1090/S0002-9939-1970-0256360-9

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Abstract:

Necessary and sufficient conditions are given in order that certain types of partially ordered continua admit a continuous selection on the hyperspace of nonempty compact connected subsets. We establish that the class of arcwise connected compacta which admit continuous selections on their space of subcontinua is a proper subclass of the dendroids. This class is also shown to be larger than the class of metrizable generalized trees.

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