Class of topologies in spaces of continuous functions

  • I. I. Perepechai


Let S be an arbitrary topological space, and let C(S) be the space of continuous real-valued functions on S. A certain class of topologies on C(S) is studied. Some cases are indicated in which topologies of a given class on C(S) are topologies of uniform convergence on compact sets of S.


Continuous Function Topological Space Uniform Convergence Arbitrary Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    J. Jameson, “Topological M-Spaces,” Math. Z.,103 (2), 139–150 (1968).Google Scholar
  2. 2.
    I. I. Perechai, “The Hahn-Banach theorem for lattice manifolds in topological M-spaces,” Vestnik Khar'k. Gos. Univ., No. 37 (1971).Google Scholar
  3. 3.
    H. Gordon, “Decomposition of linear functionals on Riesz spaces,” Duke Math. J.,27, No. 4, 597–606 (1960).Google Scholar
  4. 4.
    I. M. Gel'fand, D. A. Raikov, and G. E. Shilov, Commutative Normed Rings [in Russian], Moscow (1959).Google Scholar
  5. 5.
    A. A. Kubenskii, “On functionally closed spaces,” Dokl. Akad. Nauk SSSR,117, No. 5, 748–750 (1957).Google Scholar
  6. 6.
    E. Hewitt, “Rings of real-valued continuous functions,” Trans. Amer. Math. Soc.,64, 45–99 (1948).Google Scholar
  7. 7.
    L. Gillman, M. Henriksen, and M. Jerison, “On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions,” Proc. Amer. Math. Soc.,5, 447–460 (1954).Google Scholar
  8. 8.
    M. Katetov, “Measures in fully normal spaces,” Fund. Math.,38, 73–86 (1951).Google Scholar
  9. 9.
    S. Mrowka, “Some properties of Q-spaces,” Bull. Acad. Polon. Sci.,80, No. 10, 947–950 (1957).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • I. I. Perepechai
    • 1
  1. 1.Khar'kov State UniversityUSSR

Personalised recommendations