Alexandroff algebras and complete regularity

Reynolds, George

doi:10.1090/S0002-9939-1979-0537098-5

Alexandroff algebras and complete regularity
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Proc. Amer. Math. Soc. 76 (1979), 322-326 Request permission

Abstract:

We characterize lattice theoretically the topological notion of complete regularity and study the implications of this characterization in the setting of local lattices ($\equiv$ complete distributive lattices).

References

Additive set-functions in abstract spaces

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R. Engelking, Outline of general topology, North-Holland Publishing Co., Amsterdam; PWN—Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. Translated from the Polish by K. Sieklucki. MR 0230273
Orrin Frink, Compactifications and semi-normal spaces, Amer. J. Math. 86 (1964), 602–607. MR 166755, DOI 10.2307/2373025
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
Hugh Gordon, Rings of functions determined by zero-sets, Pacific J. Math. 36 (1971), 133–157. MR 320996
Anthony W. Hager, Real-valued functions on Alexandroff (zero-set) spaces, Comment. Math. Univ. Carolinae 16 (1975), no. 4, 755–769. MR 394547
Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9
John R. Isbell, Atomless parts of spaces, Math. Scand. 31 (1972), 5–32. MR 358725, DOI 10.7146/math.scand.a-11409
P. T. Johnstone, Topos theory, London Mathematical Society Monographs, Vol. 10, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0470019
F. E. J. Linton, Functional measure theory, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 36–49. MR 0223534
Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872
Christopher J. Mulvey, A categorical characterisation of compactness, J. London Math. Soc. (2) 17 (1978), no. 2, 356–362. MR 470930, DOI 10.1112/jlms/s2-17.2.356
George Reynolds, On the spectrum of a real representable ring, Applications of sheaves (Proc. Res. Sympos. Appl. Sheaf Theory to Logic, Algebra and Anal., Univ. Durham, Durham, 1977) Lecture Notes in Math., vol. 753, Springer, Berlin, 1979, pp. 595–611. MR 555563