On the Axiomatic Systems of Singular Cohomology Theory
Abstract
On the category of pairs of topological spaces having a homotopy type of complexes the singular (co)homology theory was axiomatically studied by J.Milnor. In particular, Milnor gave additivity axiom for a (co)homology theory and proved that any additive (co)homology theory on the given category is isomorphic to the singular (co)homology. On the other hand, the singular homology is a homology with compact support \cite{3}. In the paper \cite{6}, L. Mdzinarishvili proposed {\it partially compact support property} for a cohomology theory and gave another axiomatic characterization of the singular cohomology theory \cite{6}. In this paper, we will give additional different axiomatic characterizations of the singular cohomology theory. Moreover, we will study connections of the mentioned axiomatic systems.
Keywords
Cite
@article{arxiv.1911.05123,
title = {On the Axiomatic Systems of Singular Cohomology Theory},
author = {Anzor Beridze and Leonard Mdzinarishvili},
journal= {arXiv preprint arXiv:1911.05123},
year = {2019}
}