On the Axiomatic Systems of Singular Cohomology Theory

Anzor Beridze; Leonard Mdzinarishvili

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arXiv · 1911.05123

On the Axiomatic Systems of Singular Cohomology Theory

Anzor Beridze·Leonard Mdzinarishvili

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Abstract

On the category of pairs of topological spaces having a homotopy type of $CW$ 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.

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Anzor Beridze, Leonard Mdzinarishvili. 2019-11-12. On the Axiomatic Systems of Singular Cohomology Theory. https://arxiv.org/abs/1911.05123

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