RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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., 1995, Volume 186, Number 12, Pages 81–118 (Mi msb93)  

This article is cited in 3 scientific papers (total in 3 papers)

Extensions of the ring of continuous functions generated by the classical, rational, and regular rings of fractions as divisible hulls

V. K. Zakharov

St. Petersburg State University of Technology and Design

Abstract: The metaclassical extension generated by classical ring of quotients of the ring of continuous functions, the metarational extension generated by the rationally complete ring of quotients, and the metaregular extension generated by the regular ring of quotients, are considered along the lines of Fine–Gillman–Lambek. A new algebraic category of $c$-rings with refinement ($\equiv cr$-rings) is used to characterize them. Based on this the concept of a divisible $cr$-hull of step type is introduced. Parallel characterization are given of the metaclassical extension and the Riemann extension generated by Riemann-integrable functions, and also of the metarational and metaregular extensions and the Hausdorff–Sierpinski extension generated by semicontinuous functions.

Full text: PDF file (4744 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1995, 186:12, 1773–1809

Bibliographic databases:

UDC: 512.552
MSC: Primary 54C40, 54C30, 46J10; Secondary 54C50
Received: 18.05.1993 and 22.03.1995

Citation: V. K. Zakharov, “Extensions of the ring of continuous functions generated by the classical, rational, and regular rings of fractions as divisible hulls”, Mat. Sb., 186:12 (1995), 81–118; Sb. Math., 186:12 (1995), 1773–1809

Citation in format AMSBIB
\Bibitem{Zak95}
\by V.~K.~Zakharov
\paper Extensions of the~ring of continuous functions generated by the~classical, rational, and regular rings of fractions as divisible hulls
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 12
\pages 81--118
\mathnet{http://mi.mathnet.ru/msb93}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1376093}
\zmath{https://zbmath.org/?q=an:0871.54024}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 12
\pages 1773--1809
\crossref{https://doi.org/10.1070/SM1995v186n12ABEH000093}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UL00600011}


Linking options:
  • http://mi.mathnet.ru/eng/msb93
  • http://mi.mathnet.ru/eng/msb/v186/i12/p81

    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. Zakharov V., “Description of Extensions of Families of Continuous Functions by Means of Order Boundaries”, Dokl. Math., 71:1 (2005), 80–83  isi  elib
    2. Zakharov V.K., “Characterization of the Classical Extensions of the Family of Continuous Functions as Dedekind Hulls”, Dokl. Math., 74:3 (2006), 849–853  crossref  zmath  isi  elib
    3. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:251
    Full text:42
    References:26
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019