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 Mat. Sb. (N.S.), 1984, Volume 123(165), Number 3, Pages 369–390 (Mi msb2026)

Some applications of the functor $\varprojlim^1$

E. G. Sklyarenko

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 367–387

Bibliographic databases:

UDC: 515.14
MSC: Primary 18G10; Secondary 18G15, 15G25, 55N05, 55N07, 55N25, 55N30

Citation: E. G. Sklyarenko, “Some applications of the functor $\varprojlim^1$”, Mat. Sb. (N.S.), 123(165):3 (1984), 369–390; Math. USSR-Sb., 51:2 (1985), 367–387

Citation in format AMSBIB
\Bibitem{Skl84} \by E.~G.~Sklyarenko \paper Some applications of the functor~$\varprojlim^1$ \jour Mat. Sb. (N.S.) \yr 1984 \vol 123(165) \issue 3 \pages 369--390 \mathnet{http://mi.mathnet.ru/msb2026} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=735712} \zmath{https://zbmath.org/?q=an:0573.55005} \transl \jour Math. USSR-Sb. \yr 1985 \vol 51 \issue 2 \pages 367--387 \crossref{https://doi.org/10.1070/SM1985v051n02ABEH002864} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. G. Sklyarenko, “On the nature of homological products and duality”, Russian Math. Surveys, 49:1 (1994), 151–215
2. E. G. Sklyarenko, “Hyper(co)homology for exact left covariant functors and a homology theory for topological spaces”, Russian Math. Surveys, 50:3 (1995), 575–611
3. E. G. Sklyarenko, “On enclosure homology”, Sb. Math., 188:2 (1997), 299–306
4. A. A. Khusainov, “Razreshimost uravnenii i gipoteza kontinuuma”, Dalnevost. matem. zhurn., 4:2 (2003), 162–166
5. E. G. Sklyarenko, “On locally free Abelian groups”, Math. Notes, 77:1 (2005), 112–116
6. Sklyarenko E.G., Skordev G.S., “Integer-Valued Fixed Point Index for Compositions of Acyclic Maps”, J. Fixed Point Theory Appl., 1:1 (2007), 97–109
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