Advertisement

Lattice Realcompactifications

  • 19 Accesses

  • 2 Citations

Summary

The theory of realcompactness is generalized to a lattice setting and studied from five different viewpoints. The relationships between these viewpoints is given and applications indicated.

References

  1. [1]a)

    A. D. Alexandroff,Additive Set Functions in Abstract Spaces, Mat. Sb. (N.S.),8 (50) (1940), pp. 307–348;

  2. [1]b)

    ibid.,9 (51) (1941), pp. 563–428;

  3. [1]c)

    Mat. Sb. (N.S.),13 (55) (1943), pp. 169–238.

  4. [2]

    R. Alo -H. L. Shapiro,Wallman Compact and Real Compact Spaces, Proc. of J. Int. Symp. on the Extension Theory of Topological Structures and its Applications, Deutscher Verlag der Wissen, Berlin, 1969.

  5. [3]

    R. Alo -H. L. Shapiro,Z-realcompactifications and Normal Bases, Australian Journal of Math.,11 (1970), pp. 489–495.

  6. [4]

    G. Bachman -R. Cohen,Regular Lattice Measures and Repleteness, Communications Pure and Applied Mathematics,26 (1973), 587–599.

  7. [5]

    L. Gillman -M. Jerrison,Rings of Continuous Functions, Princeton N.J., D. Van Nostrand, 1960.

  8. [6]

    E. Hewitt,Rings of Real Valued Continuous Functions, I, Trans. Amer. Math. Soc.,64 (1948), pp. 45–99.

  9. [7]

    L. Nachbin,Topological Vector Spaces of Continuous Functions, Proc. Nat. Acad. Sci. U.S.A.,40 (1954), pp. 471–474.

  10. [8]

    A. Sultan,Generalization and Unification of Five Approach to the Stone-Čech Compactification, to appear.

  11. [9]

    V. Varadarajan,Measure and Topological Spaces, A.M.S. Translations series 2,48 (1961), pp. 161–228.

  12. [10]

    H. Wallman,Lattices and Topological Spaces, Ann. of Math., (2)42 (1938), pp. 687–697.

  13. [11]

    S. Warner,Lecture Notes on Compactifications, Reed College.

Download references

Author information

Additional information

Entrata in Redazione il 10 aprile 1974.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sultan, A. Lattice Realcompactifications. Annali di Matematica 106, 293–303 (1975) doi:10.1007/BF02415035

Download citation

Keywords

  • Lattice Setting