On the coincidence of zeroth Milnor–Thurston and singular homology
Volume 243 / 2018
Fundamenta Mathematicae 243 (2018), 109-122
MSC: Primary 55N35; Secondary 54G20.
DOI: 10.4064/fm893-6-2018
Published online: 30 July 2018
Abstract
We prove that the zeroth Milnor–Thurston homology group coincides with the zeroth singular homology group for Peano continua. Moreover, we show that the canonical homomorphism between these homology theories is not always injective. However, we prove that it is injective when the space has Borel path-components.
