Abstract
The first subsection is devoted to the definition of (ordinary) homology pro-groups H m (X;G) of an inverse system of spaces X. Their limits are the Čech homology groups \({\mathop H\limits^ \vee _m}\left( {X;G} \right).\) m (X;G). The higher derived limits limr H m ,(X; G) are also well defined. The second subsection is devoted to the construction of examples which show that, in general, these limits are non-trivial. This fact has important consequences for the strong homology groups, defined in sections 17 and 18.
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Bibliographic notes
Alexandroff, P. (1927): Une définition des nombres de Betti pour un ensemble fermé quelconque. C. R. Acad. Sci. Paris 184, 317–319
Vietoris, L. (1927): Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen. Math. Ann. 97, 454–472
Cech, E. (1932): Théorie générale de l’homologie dans un espace quelconque. Fund. Math. 19, 149–183
Dowker, C.H. (1947): Mapping theorems for non-compact spaces. Amer. J. Math. 69, 200–242
Morita, K. (1975b): Cech cohomology and covering dimension for topological spaces. Fund. Math. 87, 31–52
Mardesié, S., Segal, J. (1982): Shape theory. The inverse system approach. North - Holland, Amsterdam
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Mardešić, S. (2000). Homology pro-groups. In: Strong Shape and Homology. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13064-3_17
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DOI: https://doi.org/10.1007/978-3-662-13064-3_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08546-8
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