Retractions from C(X) onto X and Continua of Type N
We show that if a metric continuum X is of type N, then there is no a retraction from the hyperspace of subcontinua C(X) onto X, and X admits no mean. We also give an example which answers a question posed by T. J. Lee related to this topic.
W. J. Charatonik and F. Capulin, "Retractions from C(X) onto X and Continua of Type N," Houston Journal of Mathematics, University of Houston - Mathematics, Jan 2007.
Mathematics and Statistics
Keywords and Phrases
continuum; hyperspace; means; retraction; type N
Article - Journal
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