RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1973, Volume 90(132), Number 4, Pages 607–624 (Mi msb3069)  

This article is cited in 2 scientific papers (total in 2 papers)

On the axioms of homology theory

S. V. Petkova


Abstract: We give an axiomatization for homology and cohomology theory in the categories $\mathscr A$ and $\mathscr B$ of countable locally finite polyhedra and of locally compact metrizable spaces, respectively, with proper mappings; in the category $\mathscr B_0$ of metrizable compacta and continuous mappings; and (for cohomology) in the category $\mathscr B$ of locally compact metrizable spaces and arbitrary continuous mappings. In $\mathscr B$ we determine the kernel of the natural homomorphism $\varphi\colon H^n(X)\to\varprojlim H^n(C)$ over compact $C$ for a $\Pi$-additive cohomology (in particular, for Aleksandrov–Čech cohomology). Finally, we analyze the axioms of Sklyarenko (Math. Sb. (N.S.) 85(127) (1971), 201–223).
Bibliography: 6 titles.

Full text: PDF file (1978 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1973, 19:4, 597–614

Bibliographic databases:

UDC: 513.83
MSC: Primary 55B40; Secondary 55B05
Received: 23.12.1971

Citation: S. V. Petkova, “On the axioms of homology theory”, Mat. Sb. (N.S.), 90(132):4 (1973), 607–624; Math. USSR-Sb., 19:4 (1973), 597–614

Citation in format AMSBIB
\Bibitem{Pet73}
\by S.~V.~Petkova
\paper On~the axioms of homology theory
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 4
\pages 607--624
\mathnet{http://mi.mathnet.ru/msb3069}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=336737}
\zmath{https://zbmath.org/?q=an:0256.55008}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 4
\pages 597--614
\crossref{https://doi.org/10.1070/SM1973v019n04ABEH001811}


Linking options:
  • http://mi.mathnet.ru/eng/msb3069
  • http://mi.mathnet.ru/eng/msb/v132/i4/p607

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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 homology theory associated with the Aleksandrov–Čech cohomology”, Russian Math. Surveys, 34:6 (1979), 103–137  mathnet  crossref  mathscinet  zmath
    2. E. G. Sklyarenko, “On Zeeman's filtration in homology”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 477–488  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:217
    Full text:81
    References:38

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020