Abstract
We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.
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The first author would like to thank the Department of Mathematical Analysis of the University of Valencia for their hospitality during his several research visits, while this work originated.
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Dedicated to Professor Manuel Valdivia on the occasion of his 80th birthday.
Research of the first author supported in part by the Grant IAA 100 190 901 and by the Institutional Research Plan of the Academy of Sciences of Czech Republic No. AVOZ 101 905 03. The second author was supported by MTM2007-64521 from MEC.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kubiś, W., Moltó, A. Finitely fibered Rosenthal compacta and trees. RACSAM 105, 23–37 (2011). https://doi.org/10.1007/s13398-011-0006-x
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DOI: https://doi.org/10.1007/s13398-011-0006-x