Higher degrees of distributivity in lattices of continuous functions

Weinberg, Elliot Carl

doi:10.1090/S0002-9947-1962-0138569-8

Higher degrees of distributivity in lattices of continuous functions
HTML articles powered by AMS MathViewer

by Elliot Carl Weinberg

Trans. Amer. Math. Soc. 104 (1962), 334-346

DOI: https://doi.org/10.1090/S0002-9947-1962-0138569-8

PDF | Request permission

References

Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
C. H. Dowker, Local dimension of normal spaces, Quart. J. Math. Oxford Ser. (2) 6 (1955), 101–120. MR 86286, DOI 10.1093/qmath/6.1.101
P. Erdös and A. Tarski, On families of mutually exclusive sets, Ann. of Math. (2) 44 (1943), 315–329. MR 8249, DOI 10.2307/1968767
Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
Felix Hausdorff, Grundzüge der Mengenlehre, Chelsea Publishing Co., New York, N. Y., 1949 (German). MR 0031025
M. Henriksen and D. G. Johnson, On the structure of a class of archimedean lattice-ordered algebras, Fund. Math. 50 (1961/62), 73–94. MR 133698, DOI 10.4064/fm-50-1-73-94
J. R. Isbell, Zero-dimensional spaces, Tohoku Math. J. (2) 7 (1955), 1–8. MR 86285, DOI 10.2748/tmj/1178245102
R. S. Pierce, Distributivity in Boolean algebras, Pacific J. Math. 7 (1957), 983–992. MR 89180
R. S. Pierce, Distributivity and the normal completion of Boolean algebras, Pacific J. Math. 8 (1958), 133–140. MR 96604
Walter Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409–419. MR 80902
Dana Scott, The independence of certain distributive laws in Boolean algebras, Trans. Amer. Math. Soc. 84 (1957), 258–261. MR 86048, DOI 10.1090/S0002-9947-1957-0086048-7
Roman Sikorski, Boolean algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 25, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0126393
Edgar C. Smith Jr., A distributivity condition for Boolean algebras, Ann. of Math. (2) 64 (1956), 551–561. MR 86047, DOI 10.2307/1969602
E. C. Smith Jr. and Alfred Tarski, Higher degrees of distributivity and completeness in Boolean algebras, Trans. Amer. Math. Soc. 84 (1957), 230–257. MR 84466, DOI 10.1090/S0002-9947-1957-0084466-4