It is shown that for any ordinal α, there exists a T 0-space whose d-rank is equal to α.
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O. Wyler, “Dedekind complete posets and Scott topologies,” in Continuous Lattices, Proc. Conf. (Bremen, 1979), Lect. Notes Math., 871 (1981), pp. 384-389.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, Continuous Lattices and Domains, Encycl. Math. Appl., 93, Cambridge Univ. Press, Cambridge (2003).
Yu. L. Ershov, “On d-spaces,” in Theor. Comp. Sci., 224, Nos. 1/2, 59-72 (1999).
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Supported by RFBR, project No. 15-01-05114-a.
Translated from Algebra i Logika, Vol. 56, No. 2, pp. 150-163, March-April, 2017.