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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 5, Pages 1040–1071 (Mi izv918)  

This article is cited in 6 scientific papers (total in 6 papers)

Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set

E. G. Sklyarenko


Abstract: The notions of connection homology and cohomology between complementary subsets of a topological space are defined, using passage to the limit with respect to boundary-open sets, i.e., complements of pairs of closed subsets of the given complementary sets. The homology and cohomology groups so obtained enter naturally into new exact homology and cohomology sequences.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 307–335

Bibliographic databases:

UDC: 515.142.21
MSC: Primary 55N07, 55N35, 55N30; Secondary 55-02
Received: 01.03.1990

Citation: E. G. Sklyarenko, “Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set”, Izv. RAN. Ser. Mat., 56:5 (1992), 1040–1071; Russian Acad. Sci. Izv. Math., 41:2 (1993), 307–335

Citation in format AMSBIB
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\by E.~G.~Sklyarenko
\paper Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 5
\pages 1040--1071
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\zmath{https://zbmath.org/?q=an:0804.55008}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..307S}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 307--335
\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002263}
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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, “Hyper(co)homology for exact left covariant functors and a homology theory for topological spaces”, Russian Math. Surveys, 50:3 (1995), 575–611  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. E. G. Sklyarenko, “On enclosure homology”, Sb. Math., 188:2 (1997), 299–306  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. E. G. Sklyarenko, “The Thom isomorphism for nonorientable bundles”, J. Math. Sci., 136:5 (2006), 4166–4200  mathnet  crossref  mathscinet  zmath  elib  elib
    4. Yu. T. Lisitsa, “Theory of spectral sequences. II”, J. Math. Sci., 146:1 (2007), 5530–5551  mathnet  crossref  mathscinet  zmath  elib  elib
    5. E. G. Sklyarenko, “A topological version of the argument principle and Rouche's theorem”, J. Math. Sci., 146:1 (2007), 5592–5602  mathnet  crossref  mathscinet  zmath  elib
    6. Lisica J., “Strong Bonding Homology and Cohomology”, Topology Appl., 153:2-3 (2005), 394–447  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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