Ultrametrics on Cech homology groups

摘要

This paper is devoted to introducing additional structure on Cech homology groups. First, we redefine the Cech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk introduced shape groups using approximative maps. From this point on, we are able to construct complete ultrametrics on Cech homology groups. The uniform type (and then the group topology) generated by the ultrametric leads to a shape invariant which we use to deduce topological consequences. (C) 2019 Elsevier B.V. All rights reserved.