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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Concerning continuous selections


Authors: Sam B. Nadler and L. E. Ward
Journal: Proc. Amer. Math. Soc. 25 (1970), 369-374
MSC: Primary 54.55
MathSciNet review: 0256360
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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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DOI: https://doi.org/10.1090/S0002-9939-1970-0256360-9
Keywords: Dendrite, dendroid, directed space, generalized tree, selection
Article copyright: © Copyright 1970 American Mathematical Society