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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The fundamental group of a compact metric space
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by Janusz Pawlikowski PDF
Proc. Amer. Math. Soc. 126 (1998), 3083-3087 Request permission

Abstract:

We give a forcing free proof of a conjecture of Mycielski that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the continuum.
References
  • K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
  • Jan Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139–147. MR 173645, DOI 10.4064/fm-55-2-139-147
  • John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Graduate Texts in Mathematics, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0393403, DOI 10.1007/978-1-4615-9964-7
  • S. Shelah, Can the fundamental group of a nice space be e.g. the rationals, Abstracts Amer.Math. Soc. 5 (1984), 217.
  • Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
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Additional Information
  • Janusz Pawlikowski
  • Affiliation: Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Email: pawlikow@math.uni.wroc.pl
  • Received by editor(s): August 17, 1996
  • Received by editor(s) in revised form: February 26, 1997
  • Additional Notes: The author was partially supported by KBN grant 2 P03A 011 09. The author thanks J. Mycielski for introducing him to [S. Shelah, Can the fundamental group of a nice space be e.g. the rationals, Abstracts Amer. Math. Soc. 5 (1984), 217.].
  • Communicated by: Andreas R. Blass
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3083-3087
  • MSC (1991): Primary 03E15, 55Q05; Secondary 04A20, 55Q52
  • DOI: https://doi.org/10.1090/S0002-9939-98-04399-8
  • MathSciNet review: 1452818