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Proceedings of the American Mathematical Society

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Peripherally compact tree-like spaces are continuum-wise connected


Author: Ralph Bennett
Journal: Proc. Amer. Math. Soc. 39 (1973), 441-442
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1973-0315679-6
MathSciNet review: 0315679
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Abstract: The theorem stated in the title is proved, and examples are given to show the need for both peripheral compactness and tree-likeness.


References [Enhancements On Off] (What's this?)

  • [1] G. L. Gurin, Tree-like spaces, Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 (1969), no. 1, 9–12 (Russian, with English summary). MR 0253297
  • [2] V. V. Proizvolov, Peripherally bicompact tree-like spaces, Dokl. Akad. Nauk SSSR 189 (1969), 724–727 (Russian). MR 0257982
  • [3] V. V. Proizvolov, The hereditary and collective normality of a peripherally bicompact tree-like space, Dokl. Akad. Nauk SSSR 193 (1970), 1000–1003 (Russian). MR 0273577
  • [4] Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, v. 28, American Mathematical Society, New York, 1942. MR 0007095

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315679-6
Keywords: Peripherally compact, rim-compact, tree-like, continuumwise connected
Article copyright: © Copyright 1973 American Mathematical Society