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.
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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