Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The fundamental group
of a compact metric space


Author: Janusz Pawlikowski
Journal: Proc. Amer. Math. Soc. 126 (1998), 3083-3087
MSC (1991): Primary 03E15, 55Q05; Secondary 04A20, 55Q52
MathSciNet review: 1452818
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [K] K. Kuratowski, Topology. Vol. II, New edition, revised and augmented. Translated from the French by A. Kirkor, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe Polish Scientific Publishers, Warsaw, 1968. MR 0259835 (41 #4467)
    K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751 (36 #840)
  • [M] Jan Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139–147. MR 0173645 (30 #3855)
  • [O] John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 2. MR 0393403 (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] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112 (35 #1007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E15, 55Q05, 04A20, 55Q52

Retrieve articles in all journals with MSC (1991): 03E15, 55Q05, 04A20, 55Q52


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

DOI: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society