On the first homology of Peano continua

• Autorzy: Gregory R. Conner , Samuel M. Corson
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 14F35: Homotopy theory; fundamental groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 41-48

Daty

wydano

2016

Twórcy

autor

Gregory R. Conner

• Mathematics Department, Brigham Young University, Provo, UT 84602, U.S.A.

autor

Samuel M. Corson

• Mathematics Department, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, U.S.A.

Identyfikatory

DOI

10.4064/fm232-1-3