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The fundamental group of a compact metric space

Author(s): Janusz Pawlikowski
Journal: Proc. Amer. Math. Soc. 126 (1998), 3083-3087.
MSC (1991): Primary 03E15, 55Q05; Secondary 04A20, 55Q52
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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]: K. Kuratowski, Topology, Academic Press, New York, 1966, 1968. MR 41:4467; MR 36:840
[M]: J. Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139-147. MR 30:3855
[O]: J. C. Oxtoby, Measure and Category, Springer-Verlag, Berlin, 1971. MR 52:14213
[S]: S. Shelah, Can the fundamental group of a nice space be e.g. the rationals, Abstracts Amer.Math. Soc. 5 (1984), 217.
[Sp]: E. H. Spanier, Algebraic Topology, McGraw-Hill Book Company, New York, 1966. MR 35:1007

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Additional Information:

Janusz Pawlikowski
Affiliation: Department of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email: pawlikow@math.uni.wroc.pl

DOI: 10.1090/S0002-9939-98-04399-8
PII: S 0002-9939(98)04399-8
Keywords: Baire category, fundamental group, perfect set
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 \cite{S}.
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1998, American Mathematical Society


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