Geodesic
On the first homology of Peano continua
Gregory R. Conner 1   ; Samuel M. Corson 2
1 Mathematics Department Brigham Young University Provo, UT 84602, U.S.A.
2 Mathematics Department Vanderbilt University 1326 Stevenson Center Nashville, TN 37240, U.S.A.
Fundamenta Mathematicae, Tome 232 (2016) no. 1, pp. 41-48 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm232-1-3
Keywords: first homology group locally connected compact metric space either uncountable finitely generated related shelahs well known result which shows fundamental group space satisfies similar condition example space whose fundamental group uncountable whose first homology trivial showing result does follow shelahs clarify claim made pawlikowski offer proof clarification

Gregory R. Conner  1   ; Samuel M. Corson  2

1 Mathematics Department Brigham Young University Provo, UT 84602, U.S.A.
2 Mathematics Department Vanderbilt University 1326 Stevenson Center Nashville, TN 37240, U.S.A. 
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Gregory R. Conner; Samuel M. Corson. On the first homology of Peano continua. Fundamenta Mathematicae, Tome 232 (2016) no. 1, pp. 41-48. doi: 10.4064/fm232-1-3

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