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The inductive dimension of a space by its normal base

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Abstract

Properties of the large inductive dimension of a space by its normal base introduced by S. Iliadis are studied. The proposed dimension-like functions generalize both the classic dimensions Ind, Ind0 and the relative inductive dimensions I. Properties of the normal base characterizing the fulfillment of basic classic theorems of the dimension theory (sum, subset and product theorems) are found.

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References

  1. A. V. Ivanov, “The Dimension of Nonperfectly Normal Spaces,” Vestn. Mosk. Univ., Matem. Mekhan. No. 4, 21 (1976).

  2. V. V. Fedorchuk, “On the Dimension of ϰ-Metrizable Bicompacta, in Particular, of Dugundji Spaces,” Dokl. Akad. Nauk SSSR 234(1), 30 (1977).

    MathSciNet  Google Scholar 

  3. A. Ch. Chigogidze, “The Relative Dimensions of Completely Regular Spaces,” Soobsch. Akad. Gruz.SSR 85(1), 45 (1977).

    MATH  MathSciNet  Google Scholar 

  4. A. Chigogidze, “Inductive Dimensions of Completely Regular Spaces,” Comment. Math. Univ. Carol. 18(4), 623 (1977).

    MATH  MathSciNet  Google Scholar 

  5. S. D. Iliadis, Universal Spaces and Mappings (Elsevier Science B.V., North-Holland Math. Studies 198, Amsterdam, 2005).

    MATH  Google Scholar 

  6. O. Frink, “Compactifications and Semi-Normal Spaces,” Amer. J. Math. 86(3), 602 (1964).

    Article  MATH  MathSciNet  Google Scholar 

  7. P. S. Alexandrov and B. A. Pasynkov, Introduction to Dimensions Theory (Moscow, Nauka, 1973) [in Russian].

    Google Scholar 

  8. J. M. Aarts and T. Nishiura, Dimension and Extensions (Elsevier, North-Holland Math. Library, Amsterdam, 1993).

    MATH  Google Scholar 

  9. R. Engelking, Theory of Dimensions. Finite and Infinite (Sigma Ser. Pure Math. 10, Heldermann, Lemgo, 1995).

    MATH  Google Scholar 

  10. A. Ch. Chigogidze, “The Relative Dimensions,” in General Topology. Function Space and Dimension (Izd-voMGU, Moscow, 1985), pp. 67–118.

    Google Scholar 

  11. A. K. Steiner and E. F. Steiner, “Wallman and z-compactifications,” Duke Math. J. 35(2), 269 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  12. A. K. Steiner and E. F. Steiner, “Nest Generated Intersection Rings in Tychonoff Spaces,” Trans. Amer. Math. Soc. 148(2), 589 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Charalambous and V. Chatyrko, “Some Estimates of the Inductive Dimensions of the Union of Two Sets,” Topol. Appl. 146–147, 227 (2005).

    Article  MathSciNet  Google Scholar 

  14. V. V. Filippov, “The Behavior of Dimensions Under Closed Mappings,” Trudy Sem. I. G. Petrovskogo, No 3, 177 (1978).

  15. C. H. Dowker, “Inductive Dimension of Completely Normal Spaces,” Quart. J. Math. Ser. 2, 16(4), 267 (1953).

    Article  MathSciNet  Google Scholar 

  16. J. Terasawa, “Spaces N ∪ ℜ and their Dimensions,” Topol. Appl. 11, 93 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  17. E. Pol and R. Pol, “A Hereditarily Normal Strongly Zero-Dimensional Space Containing Subspaces of Arbitrary Large Dimension,” Fund. Math. 102(2), 137 (1979).

    MATH  MathSciNet  Google Scholar 

  18. B. Pasynkov, “On the Dimension of Rectangular Products,” in Proc. of Conf./Workshop Gen. Topology and Geom. Topology. University of Tsukuba, 1991 (Tsukuba, 1992), pp. 67–76.

  19. B. Pasynkov and K. Tsuda, “Product Theorems in Dimension Theory,” Tsukuba J. Math. 17(1), 59 (1993).

    MATH  MathSciNet  Google Scholar 

  20. V. V. Filippov, “The Inductive Dimension of Products of Bicompacta,” Dokl. Akad. Nauk SSSR 202(5), 1016 (1972).

    MathSciNet  Google Scholar 

  21. D. V. Malykhin “Some Properties of Topological Products,” Candidate’s Dissertation in Mathematics and Physics (MGU, Moscow, 1999).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, University of Patras, Rio Patras, 26504, Greece

    D. Georgiou, S. Iliadis & K. L. Kozlov

  2. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    D. Georgiou, S. Iliadis & K. L. Kozlov

Authors
  1. D. Georgiou
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  2. S. Iliadis
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  3. K. L. Kozlov
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Additional information

Original Russian Text © D. Georgiou, S. Iliadis, and K.L. Kozlov, 2009, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2009, Vol. 64, No. 3, pp. 7–14.

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Georgiou, D., Iliadis, S. & Kozlov, K.L. The inductive dimension of a space by its normal base. Moscow Univ. Math. Bull. 64, 95–101 (2009). https://doi.org/10.3103/S0027132209030012

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  • DOI: https://doi.org/10.3103/S0027132209030012

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