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
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.
PDF file (4744 kB)
Sbornik: Mathematics, 1995, 186:12, 1773–1809
MSC: Primary 54C40, 54C30, 46J10; Secondary 54C50
Received: 18.05.1993 and 22.03.1995
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
\paper Extensions of the~ring of continuous functions generated by the~classical, rational, and regular rings of fractions as divisible hulls
\jour Mat. Sb.
\jour Sb. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Zakharov V., “Description of Extensions of Families of Continuous Functions by Means of Order Boundaries”, Dokl. Math., 71:1 (2005), 80–83
Zakharov V.K., “Characterization of the Classical Extensions of the Family of Continuous Functions as Dedekind Hulls”, Dokl. Math., 74:3 (2006), 849–853
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200
|Number of views:|