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On the first homology of Peano continua

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Conner G., Corson S.

Fundamenta Mathematicae

2016

tom 232

nr 1

41-48

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Conner G.

1 Corson S.

1 2016

Wyniki wyszukiwania

On the first homology of Peano continua