On axiomatic characterization of Alexander-Spanier normal homology theory of general topological spaces

The Alexandroff-Čech normal cohomology theory [27], [3], [1], [2] is the unique continuous extension [36] of the additive cohomology theory [26], [4] from the category of polyhedral pairs KPol2 to the category of closed normally embedded, the so called, P-pairs of general topological spaces KTop2. I...

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Bibliographic Details
Published in:Topology and its applications 2022-08, Vol.317, p.108166, Article 108166
Main Authors: Baladze, Vladimer, Beridze, Anzor, Mdzinarishvili, Leonard
Format: Article
Language:English
Subjects:
Alexander-Spanier normal homology
Continuity of exact homology
Steenrod homology
Universal coefficient formula
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Summary:The Alexandroff-Čech normal cohomology theory [27], [3], [1], [2] is the unique continuous extension [36] of the additive cohomology theory [26], [4] from the category of polyhedral pairs KPol2 to the category of closed normally embedded, the so called, P-pairs of general topological spaces KTop2. In this paper we define the Alexander-Spanier normal cohomology theory based on all normal coverings and show that it is isomorphic to the Alexandroff-Čech normal cohomology. Using this fact and methods developed in [6] we construct an exact, the so called, Alexander-Spanier normal homology theory on the category KTop2, which is isomorphic to the Steenrod homology theory on the subcategory of compact pairs KC2. Moreover, we give an axiomatic characterization of the constructed homology theory.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108166