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Alexandroff algebras and complete regularity. (English) Zbl 0416.54015


MSC:

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06D10 Complete distributivity
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References:

[1] A. D. Alexandroff, Additive set-functions in abstract spaces, Mat. Sb. 50 (1940), 307-348; 51 (1941), 563-628; 55 (1943), 169-238. · JFM 66.0218.01
[2] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. · Zbl 0157.53001
[3] Orrin Frink, Compactifications and semi-normal spaces, Amer. J. Math. 86 (1964), 602 – 607. · Zbl 0129.38101 · doi:10.2307/2373025
[4] 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. · Zbl 0093.30001
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[9] P. T. Johnstone, Topos theory, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. London Mathematical Society Monographs, Vol. 10. · Zbl 0368.18001
[10] 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.
[11] Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. · Zbl 0232.18001
[12] Christopher J. Mulvey, A categorical characterisation of compactness, J. London Math. Soc. (2) 17 (1978), no. 2, 356 – 362. · Zbl 0393.54017 · doi:10.1112/jlms/s2-17.2.356
[13] 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.
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