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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) MR 40 #6512. MR 0253297 (40:6512)
  • [2] V. V. Proizvolov, On peripherally bicompact tree-like spaces, Dokl. Akad. Nauk SSSR 189 (1969), 724-727=Soviet Math. Dokl. 10 (1969), 1491-1493. MR 41 #2631. MR 0257982 (41:2631)
  • [3] -, On the hereditary and collective normality of a peripherally bicompact tree-like space, Dokl. Akad. Nauk SSSR 193 (1970), 1000-1003=Soviet Math. Dokl. 11 (1970), 1072-1075. MR 42 #8455. MR 0273577 (42:8455)
  • [4] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R.I., 1942. MR 4, 86. MR 0007095 (4:86b)

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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

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