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