Journal of Mathematical Sciences

, Volume 197, Issue 6, pp 741–752 | Cite as

Strong Homology Groups of Continuous Maps

  • A. Beridze


In this paper, we define coherent morphisms of chain maps and homology groups of morphisms of this type. We construct strong homology groups of continuous maps of compact metric spaces and prove that for each continuous map f : X → Y , there exists a long exact homological sequence. Moreover, we show that for each inclusion i : A → X of compact metric spaces, there exists an isomorphism \( {{\bar{H}}_n}(i)\approx {{\bar{H}}_n}\left( {X,A} \right) \).


Exact Sequence Topological Space Chain Complex Homology Group Inverse System 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsShota Rustaveli State UniversityBatumiGeorgia

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