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On the first homology of Peano continua

Volume 232 / 2016

Gregory R. Conner, Samuel M. Corson Fundamenta Mathematicae 232 (2016), 41-48 MSC: Primary 14F35; Secondary 03E15. DOI: 10.4064/fm232-1-3


We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the clarification.


  • Gregory R. ConnerMathematics Department
    Brigham Young University
    Provo, UT 84602, U.S.A.
  • Samuel M. CorsonMathematics Department
    Vanderbilt University
    1326 Stevenson Center
    Nashville, TN 37240, U.S.A.

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