Skip to main content
Log in

Representations of distributive lattices as lattices of functions

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Anderson, F. W.: Function lattices. Proc. Symposia Pure Mathematics. Volume2, 198–202 (1961).

    Google Scholar 

  2. Anderson, F. W., andR. L. Blair: Characterizations of certain lattices of functions. Pacific J. Math.9, 335–364 (1959).

    Google Scholar 

  3. Baer, R. M.: Certain homomorphisms onto chains. Arch. Math.8, 93–95 (1957).

    Google Scholar 

  4. Birkhoff, G.: On the combination of subalgebras. Proc. Cambridge Phil. Soc.29, 441–464 (1933).

    Google Scholar 

  5. Birkhoff, G.: Lattice theory. Am. Math. Soc. Colloq. Publ.25, rev. ed. (1948).

  6. Grätzer, G., andE. T. Schmidt: Characterizations of relatively complemented distributive lattices. Publ. Math., Debrecen5, 275–287 (1958).

    Google Scholar 

  7. Heider, L. J.: A characterization of function lattices. Duke Math. J.23, 297–301 (1956).

    Google Scholar 

  8. Kaplansky, I.: Lattices of continuous functions. Bull. Am. Math. Soc.53, 617–623 (1947).

    Google Scholar 

  9. Kaplansky, I.: Lattices of continuous functions. II. Am. J. Math.70, 626–634 (1948).

    Google Scholar 

  10. Łoś, J., andC. Ryll-Nardzewski: On the application of Tychonoff's theorem in mathematical proofs. Fundamenta Math.38, 233–237 (1951).

    Google Scholar 

  11. Łoś, J., andC. Ryll-Nardzewski: Effectiveness of the representation theory for Boolean algebras. Fundamenta Math.41, 49–56 (1954).

    Google Scholar 

  12. Pinsker, A. G.: A lattice characterization of function spaces (in Russian). Uspekhi Mat. Nauk (N. S.)12, 226–229 (1957).

    Google Scholar 

  13. Rubin, H., andD. Scott: Some topological theorems equivalent to the Boolean prime ideal theorem (abstract). Bull. Am. Math. Soc.60, 389 (1954).

    Google Scholar 

  14. Stone, M. H.: Applications of the theory of Boolean rings to general topology. Trans. Am. Math. Soc.41, 375–481 (1937).

    Google Scholar 

  15. Stone, M. H.: Topological representations of distributive lattices and Brouwerian logics. Cas. Mat. Fys.67, 1–25 (1937).

    Google Scholar 

  16. Tarski, A.: Some notions and methods on the borderline of algebra and metamathematics. Proc. Intern. Congr. Math. Cambridge I, 705–720 (1950).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Portions of this paper were presented, in preliminary form, at the American Mathematical Society Symposium on Lattice Theory held at Monterey, California, April 16–17, 1959; seeAnderson [1]. This research was supported by a grant from the National Science Foundation.

University of Oregon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, F.W., Blair, R.L. Representations of distributive lattices as lattices of functions. Math. Ann. 143, 187–211 (1961). https://doi.org/10.1007/BF01342978

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01342978

Keywords

Navigation