Some applications of the functor $\varprojlim^1$

E. G. Sklyarenko

Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 367-387

Résumé

The author studies the most typical forms of the connection between the functors $\varprojlim^p$ and $\operatorname{Ext}^p$; the role of the functor $\varprojlim^1$ and its cardinality properties that arise from this connection, the cardinality and other properties of the functors $\operatorname{Ext}^p$ and $\operatorname{Pext}^p$, and also of the homology and the cohomology groups of locally compact spaces. Under suitable countability restrictions, the universal coefficient formulas are investigated in situations lacking the usual connection between chains and cochains with different coefficients. The homology $H_*$ of Steenrod–Sitnikov type with locally constant coefficients is treated, as well as a definitive form of the connection between $H_*$ and the Aleksandrov–Cech homology. Bibliography: 41 titles.

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